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1. 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89, 下载量53

2. 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486, 下载量167

3. 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1326, 下载量289

4. 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799, 下载量313

5. 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1099, 下载量520

6. 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532, 下载量244

7. 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620, 下载量326

8. 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4946, 下载量654

9. chinaXiv:201704.00108 [pdf]


周伟刚; 冯倩倩; 陈仕军
分类: 数学 >> 应用数学

研究了动态围堵嫌犯问题, 假设网络边长相等, 交巡警与嫌犯的速度相等. 建立了嫌犯移动信息更新下的交巡警调度问题的0-1线性整数规划模型, 模型利用点截集条件使调度后的警力形成围堵圈, 并对嫌犯的逃跑行为建模, 由此得到了动态围堵嫌犯问题的动态模拟模型. 算例考虑分割非等边长网络的边, 然后将分割后的网络视为等边长网络.

提交时间: 2017-04-07 点击量1797, 下载量244

10. chinaXiv:201703.00918 [pdf]

Monadic NM-algebras

王军涛; 辛小龙; 贺鹏飞
分类: 数学 >> 数学(综合)

The main goal of this paper is to investigate (strong) monadic NM-algebras and to prove the (chain) completeness of the monadic NM-logic. In this paper, we introduce monadic NM-algebras: a variety of NM-algebras equipped with universal quanti#12;ers. Also, we study some properties of them and obtain some conditions under which a monadic NM-algebra becomes a monadic Boolean algebra. Besides, we show that the variety of NM-algebras are the equivalent algebraic semantics of the monadic fragment of NM predicate logic. Furthermore, we discuss relations between monadic NM-algebras and some related structures, likeness modal NMalgebras and rough approximation spaces. In addition, we introduce and investigate monadic #12;lters in monadic NM-algebras. In particular, by using monadic #12;lters on monadic NM-algebras, we characterize two kinds of monadic NM-algebras, which are simple and subdirectly irreducible. Moreover, we focus on a monadic analogous of representation theorem for NM-algebras and obtain that every strong monadic NM-algebra can be represented as subalgebras of products of linearly ordered ones. Then, we present monadic NM-logic, a system of many-valued logic capturing the tautologies of the predicate logics of nilpotent minimum t-norm and it's residua. As an application of (strong) monadic NM-algebras, we prove the (chain)completeness of monadic NM-logic. Our results constitute a crucial #12;rst step for providing a solid algebraic foundation for the one element fragment of NM predicate logic.

提交时间: 2017-03-29 点击量1276, 下载量362

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