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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. |
2. chinaXiv:201908.00121 [pdf]
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与子空间投影算法设计了一种求解特征值问题的广义共轭梯度算法, 同时也实现了相应的计算软件包. 然后对算法和计算过程进行了一系列的优化来提高算法的稳定性、计算效率和并行可扩展性, 使得本文的算法适合在并行计算环境下求解大规模稀疏矩阵的特征值. 所形成的软件包是基于Matrix-Free和Vector-Free设计的, 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具有良好的数值稳定性, 同时相比于SLEPc软件包中的LOBPCG以及Jacobi-Davidson解法器有2-6倍的效率提升. 软件包的网址: https://github.com/pase2017/GCGE-1.0. |
3. chinaXiv:201705.00826 [pdf]
Relative Entropy Minimizing-Based Theory of Intelligent Systems
Xi, GuangchengSubjects: 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. |
4. chinaXiv:201907.00015 [pdf]
周伟刚; 冯倩倩Subjects: Mathematics >> Applied Mathematics
| 研究了一道工序智能加工系统轨道式自动引导车（RGV）调度问题. 该问题为2018年全国大学生数学建模竞赛B题的一部分. 系统由一辆轨道式自动引导车和若干台计算机数控机床(CNC)等部件组成, RGV操控多台CNC完成多个物料加工, RGV调度方案决定了系统的效率. 以 RGV的移动路径为决策变量, 以RGV在CNC上的操作结束时刻为时间节点, 以物料加工剩余时间为状态变量, 给出了问题的数学模型, 但模型中的部分参数以决策变量为下标. 通过定义新的变量和约束, 将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. 最后给出了算例, 说明了模型的正确性和可操作性. |
5. chinaXiv:201904.00081 [pdf]
何沧平Subjects: Mathematics >> Computational Mathematics.
| 本文提出一个名为接圆回归的点击率预测新方法，尝试替代常用的因子分解机(FM)。接圆回归用超平面拼接出一个封闭凸多面体，圈出正样本，有直观的几何解释， 能从任意初始值一次收敛到全局最优解。 拟合出来的曲面Lipschitz连续，变化平缓。在人工设计的星环集、双堆集、双月集上，接圆回归的分类准确性、解释性、平滑性全面超过FM。在同量级参数量、计算量 的条件下，接圆回归在Avazu集和Criteo集上的AUC超过FM。 |
6. chinaXiv:201705.00829 [pdf]
Entropy-partition of Complex Systems and Emergence of Human Brain’s Consciousness
Xi GuangchengSubjects: 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 Hits2048， Downloads1065， Comment 0
7. chinaXiv:201803.01556 [pdf]
Gibbsian representation of knowledge in infinite dimensional random neural networks(IDRNN)
xi guangchengSubjects: 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. |
8. chinaXiv:201810.00001 [pdf]
彭俊金Subjects: Physics >> The Physics of Elementary Particles and Fields
| 本文系统地探讨了霍奇星算子与外微分算符作用于任意微分形式场时两者的一般组合规律。首先，找到了保持微分形式场的次不变的两个组合算符，并通过二者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外微分算符进行组合时，作者导出了所有形式上彼此互异的组合算符的统一表达式，这些表达式由单个霍奇星算子与外微分算符以及二者的任选两个的非零组合构成。在此基础上，分析了所有算符之间的相互作用关系，并根据这些算符对微分形式的次的改变情况，对它们进行了具体分类。最后，作为一个应用，作者详细讨论了如何由次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。 |
9. chinaXiv:201810.00100 [pdf]
李鸿仪Subjects: Mathematics >> Logic
| 为了从根本上消灭存在于数学基础中的各种悖论，使数学建筑在高度可靠的基础上，发现形式逻辑只能用于同一律，矛盾律和排中律这三大规律都成立的讨论域 (称为可行域) 内，否则就会产生包括悖论在内的各种错误，而在形式逻辑的适用范围即可行域内，只要前提可靠，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一些历史上比较著名的悖论的形成原因，同时指出了数学基础中皮亚诺公理的应用和康托尔定理、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统一的定义自然数、有理数和无理数的建议。 |
10. chinaXiv:201809.00178 [pdf]
Regularity for a minimum problem with free boundary in Orlicz spaces
Jun Zheng; Leandro S. Tavares; Claudianor O. AlvesSubjects: 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 $\lambda_{+}>0$. |
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