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1. chinaXiv:201909.00015 [pdf]

Analytical expressions of copositivity for 4th order symmetric tensors and applications

宋义生; 祁力群
Subjects: Mathematics >> Control and Optimization.

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

submitted time 2019-08-30 Hits97, Downloads40, Comment 0

2. chinaXiv:201908.00121 [pdf]

一中求解特征值问题的广义共轭梯度算法

谢和虎; 张宁; 李瑜; 徐然; 游春光
Subjects: Mathematics >> Computational Mathematics.

本文基于阻尼块反幂法和分支空间投影算法设计了同种求解特征值问题的广义共轭梯度算法, 并且为实现了相应的计算软件包. 下一场对算法和计算过程进行了一连串的优化来提高算法的安定、计算效率和相互可扩展性, 使得本文的算法适合于相互计算环境下求解大规模稀疏矩阵的特征值. 所形成的软件包是根据Matrix-Free和Vector-Free计划的, 可以应用于任意的矩阵向量结构. 针对几种典型矩阵的测试结果表明本文的算法和软件包不但有良好的数值稳定性, 并且相比于SLEPc软件包中的LOBPCG和Jacobi-Davidson消除法器有2-6倍的频率提升. 软件包的网址: https://github.com/pase2017/GCGE-1.0.

submitted time 2019-08-27 Hits157, Downloads71, Comment 0

3. chinaXiv:201705.00826 [pdf]

Relative Entropy Minimizing-Based Theory of Intelligent Systems

Xi, Guangcheng
Subjects: Mathematics >> Statistics and Probability

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.

submitted time 2019-07-21 Hits2231, Downloads896, Comment 0

4. chinaXiv:201907.00015 [pdf]

共同工序智能加工系统 RGV 调度模型

周伟刚; 冯倩倩
Subjects: Mathematics >> Applied Mathematics

研究了共同工序智能加工系统则式自动引导车(RGV)调度问题. 该问题吗2018年全国大学生数学建模竞赛B写的部分. 系统由一辆轨道式自动引导车和几尊计算机数控机床(CNC)相当部件组成, RGV操控多尊CNC完成多只物料加工, RGV调度方案决定了系统的频率. 因为 RGV的移动路径为决策变量, 因为RGV在CNC达到的操作结束时刻为日节点, 因为物料加工剩余时间为状态变量, 被来了问题的数学模型, 但是模型中的部分参数以决定变量为下标. 通过定义新的变量和约束, 以模型修改为不含变量下标和分段函数的非线性混合整数规划模型. 末了被来了算例, 说明了模型的正确和可操作性.

submitted time 2019-07-16 Hits1888, Downloads123, Comment 0

5. chinaXiv:201904.00081 [pdf]

连到回归

何沧平
Subjects: Mathematics >> Computational Mathematics.

本文提出一个名接到回归的点击率预测新方法,尝试替代常用的因子分解机(FM)。连到回归用过平面拼接出一个封凸多面体,围绕出正样本,发生直观的若干解释, 能够从任意初始值一次收敛到全局最优解。 拟合出来的曲面Lipschitz一连,变和。在人工设计的星环集、双堆集、双月集达成,连到回归的分类准确性、说性、平滑性全面超过FM。在和量级参数量、计算量 的标准下,连到回归在Avazu聚拢和Criteo聚拢上的AUC超越FM。

submitted time 2019-04-10 Hits1952, Downloads285, Comment 0

6. chinaXiv:201705.00829 [pdf]

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

Xi Guangcheng
Subjects: Mathematics >> Statistics and Probability

The three frameworks for theories of consciousness taken moust seriously by neuroscientists are that consciousness is a biological state of the brain,the global workspace perspective,and the perspective of higher state. Consciousness is discussed from viewpoint of theory of Entropy—partition of complex system in present article. Human brain’s system self-organizably and adaptively implements partition、aggregation and integration, and consciousness emerges.

submitted time 2019-01-10 Hits2087, Downloads1081, Comment 0

7. chinaXiv:201803.01556 [pdf]

Gibbsian representation of knowledge in infinite dimensional random neural networks(IDRNN)

xi guangcheng
Subjects: Mathematics >> Statistics and Probability

Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential.

submitted time 2018-11-07 Hits1521, Downloads690, Comment 0

8. chinaXiv:201810.00001 [pdf]

霍奇星算子与他微分算符的结合规律

彭俊金
Subjects: Physics >> The Physics of Elementary Particles and Fields

本文系地探索了霍奇星算子与他微分算符作用于任意微分形式场时两者的相似组合规律。首先,找到了保障微分形式场的差不变的少只结合算符,连通过双方的线性组合得到了一个新算符。其次,当由任意数目的霍奇星算子与他微分算符进行结合时,作者导出了有形式上相互互异的结合算符的合并表达式,这些表达式由单个霍奇星算子与他微分算符以及两岸的任选两只之非零组合成。在这个基础上,分析了有算符之间的相互作用关系,连根据这些算符对微分形式的差的改变情况,针对它进行了实际分类。末了,作为一个用,作者详细讨论了怎样由坏相同的微分形式的线性组合来构造电磁场的麦克斯韦方程。

submitted time 2018-10-08 Hits1693, Downloads572, Comment 0

9. chinaXiv:201810.00100 [pdf]

逻辑学及其在数学基础应用中的一些问题

李鸿仪
Subjects: Mathematics >> Logic

为打根本上除存在于数学基础中的各种悖论,如果数学建筑于高度可靠的基础上,察觉形式逻辑只能用于同一律,矛盾律和排中律这三大规律还建立的议论地区 (称可行域) 外,否则即会发生包括悖论在内的各种错误,如果在形式逻辑的适用范围就可行域内,如果前提可靠,推导严格,悖论是不存在的。根据该结论,分析了说谎者悖论和理发师悖论等部分历史上比著名的悖论的形成原因,并且指出了数学基础中皮亚诺公理的使用和康托尔定理、区间套和对角线法证明中的一些逻辑错误,提出了能够避免这些错误的合并的定义自然数、有理数和无理数的建议。

submitted time 2018-09-28 Hits998, Downloads530, Comment 0

10. chinaXiv:201809.00178 [pdf]

Regularity for a minimum problem with free boundary in Orlicz spaces

Jun Zheng; Leandro S. Tavares; Claudianor O. Alves
Subjects: Mathematics >> Mathematics (General)

The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_{\Omega}(G(|\nabla u|)+qF(u^+)+hu+\lambda_{+}\chi_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions $ W^{1,G}(\Omega)$ with $ u-\varphi\in W^{1,G}_{0}(\Omega)$, for a given function $\varphi$, where $W^{1,G}(\Omega)$ is the class of weakly differentiable functions with $\int_{\Omega}G(|\nabla u|)\text{d}x<\infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $\infty$. Given functions $q,h$ and constant $\lambda_+\geq 0$, we address several regularities for minimizers of $\mathcal {J}(u)$, including local $C^{1,\alpha}-$, and local Log-Lipschitz continuities for minimizers of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. We also establish growth rate near the free boundary for each non-negative minimizer of $\mathcal {J}(u)$ with $\lambda_+=0$, and $\lambda_+>0$ respectively. Furthermore, under additional assumption that $F\in C^1([0,+\infty); [0,+\infty))$, local Lipschitz regularity is carried out for non-negative minimizers of $\mathcal {J}(u)$ with $\lambda_{+}>0$.

submitted time 2018-09-23 Hits3736, Downloads469, Comment 0

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