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1. chinaXiv:201712.00241 [pdf]

圈图超平面配置的导模及其自由解.pdf

Wu Jun
分类: 数学 >> 离散数学和组合数学

本文利用代数和组合的相关理论对超平面配置理论的自由性做出了相关研究,给出圈图所对应的图配置的生成元和导模的具体形式,并以图论的形式对圈图配置的导模及其自由解做出相关的组合解 释.

提交时间: 2017-12-22 点击量86下载量59 评论 0

2. chinaXiv:201712.02142 [pdf]

Upper bounds for Z$_1$-eigenvalues of generalized Hilbert tensors

孟娟; 宋义生
分类: 数学 >> 数学(综合)

In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}+\lambda},\ \lambda\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=0,1,2,\cdots,n,\cdots, $$ and proved that its $Z_1$-spectral radius is not larger than $\pi$ for $\lambda>\frac{1}{2}$, and is at most $\frac{\pi}{\sin{\lambda\pi}}$ for $\frac{1}{2}\geq \lambda>0$. Besides, the upper bound of $Z_1$-spectral radius of an $m$th-order $n$-dimensional generalized Hilbert tensor $\mathcal{H}_\lambda^n$ is obtained also, and such a bound only depends on $n$ and $\lambda$.

提交时间: 2017-12-12 点击量331下载量68 评论 0

3. chinaXiv:201712.01969 [pdf]

红外成像灰度随距离变化的李群表达

李晨曦; 史泽林; 刘云鹏
分类: 物理学 >> 电磁学、光学、声学、传热、经典力学和流体动力学
分类: 数学 >> 数学(综合)

大气对红外辐射传输的影响引起的红外成像灰度变化,是红外目标跟踪应用需要应对的问题。本文的研究目的是对红外成像灰度变化规律进行李群建模,对设计高效、鲁棒的目标跟踪算法有重要意义。首先分析了红外辐射传输模型,并结合红外成像机理,得到红外成像灰度变化模型。进一步从理论上证明了大气影响下红外成像灰度变化规律符合李群结构,提出了红外图像灰度动态变化的一种非欧数学表征。最后根据红外成像灰度变化模型对不同环境下采集到的外场实验数据进行拟合,回归分析结果表明了该模型的准确性,进而说明了本文对红外成像灰度变化规律进行李群表达的合理性。

提交时间: 2017-11-26 点击量504下载量146 评论 0

4. chinaXiv:201711.02631 [pdf]

Partial generalizations of some Conjectures in locally symmetric Lorentz spaces

孙忠洋
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134下载量114 评论 0

5. chinaXiv:201711.02399 [pdf]

对焦分类方法

何沧平
分类: 数学 >> 计算科学理论

本文提出一个名为对焦分类的线性分类方法,尝试替代经典的逻辑回归。对焦分类能够从数学论证上保证法向量有界,有直观的几何解释,方便选取更接近最优值的参数初值,在手写数字图像数据集上的分类正确率、收敛速度均显著优于逻辑回归,参数初值即使分类正确率达到了97.31%。

提交时间: 2017-11-17 点击量1430下载量643 评论 0

6. 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400下载量334 评论 0

7. 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740下载量389 评论 0

8. 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2265下载量447 评论 0

9. chinaXiv:201706.00751 [pdf]

基于加权回归分析以支持向量机为风险控制的多因子选股模型实证研究

李皓辰; 闫昱; 经玲; 王燕飞
分类: 数学 >> 数学(综合)

考虑股票选取的多因子问题,在传统模型的基础上,利用MATLAB软件建立使用加权回归(权由日期和涨跌幅综合决定)的股票基本面指标、技术指标对相对收益率的多因子模型,并且引入支持向量机作为风控,最终获得了一个收益较好的量化投资模型。

提交时间: 2017-06-22 点击量1777下载量599 评论 0

10. 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1509下载量892 评论 0

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