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1. chinaXiv:201711.02631 [pdf]

Partial generalizations of some Conjectures in locally symmetric Lorentz spaces

分类: 数学 >> 几何与拓扑

这篇文章中,首先给出了局部对称Lorentz空间中线性 Weingarten类空超曲面的数量曲率和平均曲率的关系。进而,我们研究了局部对称Lorentz空间中满足一定曲率的完备或者紧致线性 Weingarten类空超曲面,通过修改Cheng-Yau的算子,给出了一些新的估计。最终,我们在局部对称Lorentz空间中给出了一些猜想的部分推广。

提交时间: 2017-11-23 点击量29下载量18 评论 0

2. chinaXiv:201711.02399 [pdf]


分类: 数学 >> 计算科学理论


提交时间: 2017-11-17 点击量891下载量244 评论 0

3. chinaXiv:201708.00246 [pdf]

From limited-aperture to full-aperture

Xiaodong Liu
分类: 数学 >> 计算数学

Many numerical methods have been proposed in the last 30 years for inverse problems. While very successful in many cases, progress has lagged in other areas of applications which are forced to rely on {\em limited-aperture} measurements. In this paper, we introduce some techniques to retrieve the other data that can not be measured directly. We consider the inverse acoustic scattering of time harmonic plane waves and take the scattering amplitude to be the measurements. Assume that the scattering amplitude can only be measured with observation directions restricted in $S^{n-1}_0$, which is compactly supported in the unit sphere. Based on the reciprocity relation of the scattering amplitude, we prove a special symmetric structure of the corresponding multi-static response matrix. This will also be verified by numerical examples. Combining this, with the help of the Green's formula for the scattered field, we introduce an iterative scheme to retrieve approximate {\em full-aperture} scattering amplitude. As an application, using a recently proposed direct sampling method [28], we consider the fast and robust sampling methods with {\em limited-aperture} measurements. Some numerical simulations are conducted with noisy data, and the results will further verify the effectiveness and robustness of the proposed data retrieval method and of the sampling method for inverse acoustic scattering problems.

提交时间: 2017-08-22 点击量157下载量103 评论 0

4. chinaXiv:201707.00007 [pdf]

B tensors and tensor complementarity problems

Yisheng Song; Wei Mei
分类: 数学 >> 控制和优化

In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we present that each B tensor is strictly semi-positive and each B$_0$ tensor is semi-positive. Subsequencely, the strictly lower and upper bounds of different operator norms are given for two positively homogeneous operators defined by B tensor. Finally, with the help of the upper bounds of different operator norms, we show the strcitly lower bound of solution set of tensor complementarity problem with B tensor. Furthermore, the upper bounds of spectral radius and $E$-spectral radius of B (B$_0$) tensor are obtained, respectively, which achieves our another objective. In particular, such the upper bounds only depend on the principal diagonal entries of tensors.

提交时间: 2017-07-25 点击量566下载量228 评论 0

5. chinaXiv:201611.00887 [pdf]

Infinite and finite dimensional generalized Hilbert tensors

Wei Mei; Yisheng Song
分类: 数学 >> 数学(综合)

In this paper, we introduce the concept of an m-order n-dimensional generalized Hilbert tensor \mathcal{H}_{n}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}}), \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}-m+a},\ a\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=1,2,\cdots,n, and show that its H-spectral radius and its Z-spectral radius are smaller than or equal to M(a)n^{m-1} and M(a)n^{\frac{m}{2}}, respectively, here M(a) is a constant only dependent on a. Moreover, both infinite and finite dimensional generalized Hilbert tensors are positive definite for a\geq1. For an m-order infinite dimensional generalized Hilbert tensor $\mathcal{H}_{\infty} with a>0, we prove that \mathcal{H}_{\infty} defines a bounded and positively (m-1)-homogeneous operator from l^{1} into l^{p}\ (1

提交时间: 2017-07-03 点击量1796下载量321 评论 0

6. chinaXiv:201706.00751 [pdf]


李皓辰; 闫昱; 经玲; 王燕飞
分类: 数学 >> 数学(综合)


提交时间: 2017-06-22 点击量1185下载量409 评论 0

7. chinaXiv:201705.00968 [pdf]

Using associative neural network to interpret syndromes of Traditional Chinese Medicine

Xi, Guangcheng; Chen, Jianxin; Yi,JianQiang;
分类: 数学 >> 建模与仿真

Millions of people benefit form Traditional Chinese Medicine(TCM) every day. Unfortunately, till now, TCM has not been accepted as science by world, especially western people. Bian Zheng Lun Zhi is distillation of TCM. Syndrome is key in system of Bian Zheng Lun Zhi. Study about the syndrome is core of study of basic theory of TCM. We creatively interpret TCM through a view of cognitive science and take syndromes of TCM as concepts of brain. This paper try to introduce syndrome to western people, in order to let western people understand our viewpoints more easily, the best method is to adopt a manner that is easily understood by them, already exists, and has been thought to be right. So we employ neural network presented by foreign people as brain model instead of network presented by us Using two classic case of TCM, we successfully clarify the three main properties of syndrome in TCM.

提交时间: 2017-05-25 点击量1208下载量610 评论 0

8. chinaXiv:201705.00826 [pdf]

Relative Entropy Minimizing-Based Theory of Intelligent Systems

Xi, Guangcheng
分类: 数学 >> 统计和概率

Based on the point of view of neuroethology and cognition-psychology, general frame of theory for intelligent systems is presented by means of principle of relative entropy minimizing in this paper. Cream of the general frame of theory is to present and to prove basic principle of intelligent systems: entropy increases or decreases together with intelligence in the intelligent systems. The basic principle is of momentous theoretical significance and practical significance .From the basic principle can not only derive two kind of learning algorithms (statistical simulating annealing algorithms and annealing algorithms of mean-field theory approximation) for training large kinds of stochastic neural networks,but also can thoroughly dispel misgivings created by second law of thermodynamics on 'peoplespsychology ,hence make one be fully confident of facing life.Because of Human society, natural world, and even universe all are intelligent systems.

提交时间: 2017-05-13 点击量579下载量276 评论 0

9. chinaXiv:201705.00829 [pdf]

Entropy-partition of Complex Systems and Emergence of Human Brain’s Consciousness

Xi, Guangcheng
分类: 数学 >> 统计和概率

Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system. Human brain’s system self-organizably and adaptively implements partition, aggregation, integration, and consciousness emerges.

提交时间: 2017-05-13 点击量674下载量366 评论 0

10. chinaXiv:201704.00218 [pdf]


谭伟杰; 冯西安
分类: 数学 >> 应用数学

摘要:传统子空间类方法依赖于阵列相关矩阵,在阵列中阵元出现失效的情况下,相关矩阵将会秩亏,子空间类方法将会失效。针对该问题,本文从协方差拟合准则出发,将协方差矩阵的 Toeplitz 结构作为约束,基于低秩矩阵重构的原理来恢复协方差矩阵,而后采用子空间类方法来进行目标的方位估计。在阵元失效情况下,该方法能有效重构阵列协方差矩阵,恢复失效阵元的自由度,解决失效阵元情况下高精度目标方位估计的问题。数值仿真表明,该方法在阵元失效条件下,能够恢复损伤阵列到正常阵列条件下的性能,尤其是对于多个目标的情况,该方法表现出更优的性能。

提交时间: 2017-04-19 点击量5718下载量797 评论 0

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