分类: 数学 >> 代数与数论 提交时间: 2016-05-19
摘要: For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has order predicted by the Birch and Swinnerton-Dyer conjecture.
分类: 数学 >> 数学(综合) 提交时间: 2016-07-05
摘要: In this paper, the Pazy's Fixed Point Theorems of monotone $\alpha-$nonexpansive mapping $T$ are proved in a uniformly convex Banach space $E$ with the partial order ``$\leq$". That is, we obtain that the fixed point set of $T$ with respect to the partial order ``$\leq$" is nonempty whenever the Picard iteration $\{T^nx_0\}$ is bounded for some comparable initial point $x_0$ and its image $Tx_0$. When restricting the demain of $T$ to the cone $P$, a monotone $\alpha-$nonexpansive mapping $T$ has at least a fixed point if and only if the Picard iteration $\{T^n0\}$ is bounbed. Furthermore, with the help of the properties of the normal cone $P$, the weakly and strongly convergent theorems of the Picard iteration $\{T^nx_0\}$ are showed for finding a fixed point of $T$ with respect to the partial order ``$\leq$" in uniformly convex ordered Banach space.
分类: 数学 >> 应用数学 提交时间: 2016-07-07
摘要: 自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅摘要:自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅限于逆向递推法和数列递推法。本文首先借鉴这两种方法建立一阶差分模型;而后,考虑到每个海盗不是绝对理性的,等级高的海盗需要依赖等级低一级的海盗的决策而做出最优决策,建立二阶时滞差分模型,在数学原理上对 PG 做深入分析:当τ= 0 时,与实际情况偏差较大;当时滞量 τ=1 时,模型的解和一阶差分模型的解一致,即在现实生活中也存在着做决策时直接咨询自己的第一副手的社会群体。从而,在现代分析方法的层次上,本文给出一个 PG 的新的合理的数学解释。
分类: 数学 >> 控制和优化 分类: 数学 >> 计算数学 提交时间: 2016-07-11
摘要: In this paper, we construct and analyze an efficient m-step Levenberg-Marquardt method for nonlinear equations. The main advantage of this method is that the m-step LM method could save more Jacobian calculations with frozen $(J_k^TJ_k+\lambda_kI)^{-1}J_k^T$ at every iteration. Under the local error bound condition which is weaker than nonsingularity, the m-step LM method has been proved to have $(m+1)$th convergence order. The global convergence has also been given by trust region technique. Numerical results show that the m-step LM method is efficient and could save many calculations of the Jacobian especially for large scale problems.
分类: 数学 >> 控制和优化 提交时间: 2016-08-30
摘要: In this paper necessary conditions and sufficient conditions are given for a linear operator to be a positive operators of an Extended Lorentz cone. Similarities and differences with the positive operators of Lorentz cones are investigated.
分类: 数学 >> 数学(综合) 提交时间: 2016-11-09
摘要: In this paper, the $m-$order infinite dimensional Hilbert tensor (hypermatrix) is intrduced to define an $(m-1)$-homogeneous operator on the spaces of analytic functions, which is called Hilbert tensor operator. The boundedness of Hilbert tensor operator is presented on Bergman spaces $A^p$ ($p>2(m-1)$). On the base of the boundedness, two positively homogeneous operators are introduced to the spaces of analytic functions, and hence the upper bounds of norm of such two operators are found on Bergman spaces $A^p$ ($p>2(m-1)$). In particular, the norms of such two operators on Bergman spaces $A^{4(m-1)}$ are smaller than or equal to $\pi$ and $\pi^\frac1{m-1}$, respectively.
分类: 数学 >> 控制和优化 提交时间: 2016-12-16
摘要: Although the Karush-Kuhn-Tucker conditions suggest a connection between a conic optimization problem and a complementarity problem, it is difficult to find an accessible explicit form of this relationship in the literature. This note will present such a relationship.
分类: 数学 >> 数学(综合) 提交时间: 2017-03-29
摘要: 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.
分类: 数学 >> 应用数学 提交时间: 2017-04-07
摘要: 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.
分类: 数学 >> 建模与仿真 提交时间: 2017-05-25
摘要: 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.
分类: 数学 >> 数学(综合) 提交时间: 2017-06-22
摘要: 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。
分类: 数学 >> 数学(综合) 提交时间: 2017-07-03
摘要: 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 $\mathcal{H}_{\infty} with a>0, we prove that \mathcal{H}_{\infty} defines a bounded and positively (m-1)-homogeneous operator from l^{1} into l^{p}\ (1
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分类: 数学 >> 控制和优化 提交时间: 2017-07-25
摘要: In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we present that each B tensor is strictly semi-positive and each B$_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.
分类: 数学 >> 计算数学 分类: 数学 >> 应用数学 提交时间: 2017-08-22
摘要: 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.
分类: 数学 >> 计算科学理论 提交时间: 2017-11-17
摘要: 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%。
分类: 数学 >> 几何与拓扑 提交时间: 2017-11-23
摘要: 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。
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: 信息科学与系统科学 >> 信息科学与系统科学基础学科 分类: 数学 >> 数学(综合) 提交时间: 2017-11-26
摘要: 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。
分类: 数学 >> 数学(综合) 提交时间: 2017-12-12
摘要: 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 $\lambda$.
分类: 数学 >> 离散数学和组合数学 提交时间: 2017-12-22
摘要: 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.
分类: 数学 >> 计算数学 提交时间: 2018-03-22
摘要: 本文通过严格数学分析找出了逻辑回归过拟合的成因:边界样本的损失贡献比重大且随法向量增长而加速增大、边界样本分布散乱,顺便理清了正则项的作用机理。 利用过拟合机制,本文提出一种反拉方法,既能缓解过拟合,又能减少训练步数,在MNIST数据集上实现加速38.25倍,在CIFAR10数据集上实现加速5.61倍。