分类: 数学 >> 统计和概率 分类: 统计学 >> 数理统计学 分类: 信息科学与系统科学 >> 信息科学与系统科学基础学科 提交时间: 2024-05-22
摘要: 统计独立性是统计学和机器学习领域的基础性概念,如何表示和度量统计独立性是该领域的基本问题。Copula理论提供了统计相关关系表示的理论工具,而Copula熵理论则给出了度量统计独立性的概念工具。本文综述了Copula熵的理论和应用,概述了其基本概念定义、定理和性质,以及估计方法。介绍了Copula熵研究的最新进展,包括其在统计学的十个基本问题(结构学习、关联发现、变量选择、因果发现、系统辨识、时延估计、域自适应、正态性检验、双样本检验和变点检测等)上的理论应用。讨论了理论应用之间的联系,以及其对应的深层次的相关性和因果性概念之间的联系,并将Copula熵的(条件)独立性度量框架与基于核函数和距离相关的同类框架进行了理论对比。通过仿真和实际数据实验评估验证了Copula熵方法体系相对于同类方法的实际优越性。简述了Copula熵在理论物理学、天体物理学、地球物理学、理论化学、化学信息学、材料学、水文学、气候学、气象学、环境学、生态学、动物形态学、农学、认知神经学、运动神经学、计算神经学、心理学、系统生物学、生物信息学、临床诊断学、老年医学、精神病学、公共卫生学、经济学、管理学、社会学、教育学、计算语言学、新闻传播学、法学、政治学、军事学、情报学,以及能源工程、食品工程、土木建筑、交通运输、制造工程、可靠性工程、冶金工程、化学工程、航空航天、兵器工程、车辆工程、电子工程、通信工程、高性能计算、信息安全、测绘遥感、海洋工程和金融工程等领域的实际应用。
分类: 数学 >> 数学(综合) 提交时间: 2024-05-16
摘要: 五千年的我国传统文化是国家与民族继承与发展的基础。弘扬我国优秀的传统文化有利于增进当代大学生的文化自信。如何将我国灿烂的传统文化有机地融入到《高等数学》的枯燥的学习中去,如何提高当代大学生对这门课程的兴趣,以及树立他们的文化自信,上述种种,在当前都值得我们去探究。本文基于此出发点,以一个重要的知识点——分部积分的思政教学为例,我们给出了中国传统文化中的若干典型形象在《高等数学》课程中的一个应用。另外,可以发现笔者的思政教学,有效地提高了学生对这门课的学习兴趣和学习效果。
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-03-27
摘要: Let f(n) be the maximum number of edges in a graph on n vertices in which no two cycles have the same length. Erd¨os raised the problem of determining f(n). Erd¨os conjectured that there exists a positive constant c such that ex(n, C2k) ≥ cn1+1/k. Haj´os conjecture that every simple even graph on n vertices can be decomposed into at most n/2 cycles. We present the problems, conjectures related to these problems and we summarize the know results. We do not think Haj´os conjecture is true.
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-03-27
摘要: The set of all non-increasing nonnegative integers sequence π = (d(v1), d(v2), ..., d(vn)) is denoted by NSn. A sequence π ∈ NSn is said to be graphic if it is the degree sequence of a simple graph G on n vertices, and such a graph G is called a realization of π. The set of all graphic sequences in NSn is denoted by GSn. A graphical sequence π is potentially H-graphical if there is a realization of π containing H as a subgraph, while π is forcibly H-graphical if every realization of π contains H as a subgraph. Let Kk denote a complete graph on k vertices. Let Km −H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of Km). This paper summarizes briefly some recent results on potentially Km −G-graphic sequences and give a useful classification for determining σ(H, n).
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-03-26
摘要: In 1975, P. Erd {o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different lengths. In this paper, it is proved that $$f(n) geq n+32t-1$$ for $t=27720r+169 , (r geq 1)$ and $n geq frac{6911}{16}t^{2}+ frac{514441}{8}t- frac{3309665}{16}$. Consequently, $ liminf sb {n to infty} {f(n)-n over sqrt n} geq sqrt {2 + {2562 over 6911}}.$
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-03-26
摘要: In 1975,P.Erd {o}sproposedtheproblemofdeterminingthemaximumnumber$f(n)$ofedgesinagraphwith$n$verticesinwhichanytwocyclesareofdifferentlengths.Inthispaper,itisprovedthat$$f(n) geqn+ frac{107}{3}t+ frac{7}{3}$$for$t=1260r+169 , (r geq1)$and$n geq frac{2119}{4}t^{2}+87978t+ frac{15957}{4}$.Consequently,$ liminf sb{n to infty}{f(n)-n over sqrtn} geq sqrt{2+ frac{7654}{19071}},$whichisbetterthanthepreviousbounds$ sqrt2$ Y.Shi,DiscreteMath.71(1988),57-71 ,$ sqrt{2.4}$ C.Lai,Australas.J.Combin.27(2003),101-105 .Theconjecture$ lim_{n rightarrow infty}{f(n)-n over sqrtn}= sqrt{2.4}$isnottrue.
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-03-26
摘要: 设f(n) 是没有等长圈的n个顶点的图的最大可能边数。确定f(n)的问题由Erdos在1975年提出。本文给出了f(n)的下界。
分类: 数学 >> 数学(综合) 提交时间: 2024-03-01
摘要: In this paper, the main aim is to demonstrate the boundedness for commutators of fractional maximal function and sharp maximal function in the context of the p-adic version of Orlicz spaces, where the symbols of the commutators belong to the p-adic version of Lipschitz space, whereby some new characterizations for Λβ(Qnp) spaces are given.
分类: 数学 >> 数学(综合) 提交时间: 2024-03-01
摘要: In this article, the main aim is to introduce the grand variable Herz space over the p-adic fields and demonstrate the boundedness for fractional integral operator, fractional maximal operator in the context of the grand p-adic version of Herz-Morrey spaces with variable exponent, as well as the Lipschitz estimates for the commutators of fractional integral operator, fractional maximal operator, and sharp maximal function on the grand p-adic version of Herz-Morrey spaces with variable exponent.
分类: 数学 >> 几何与拓扑 提交时间: 2024-02-28
摘要: In this paper, we study biharmonic Riemannian submersions $ pi:M^2 times r to (N^2,h)$ from a product manifold onto a surface and obtain some local characterizations of such biharmonic maps. Our results show that when the target surface is flat, then a proper biharmonic Riemannian submersion $ pi:M^2 times r to (N^2,h)$ is locally a projection of a special twisted product, and when the target surface is non-flat, $ pi$ is locally a special map between two warped product spaces with a warping function that solves a single ODE. As a by-product, we also prove that there is a unique proper biharmonic Riemannian submersion $H^2 times r to r^2$ given by the projection of a warped product.
分类: 数学 >> 代数与数论 提交时间: 2024-02-23
摘要: 本文以拓扑Abel群的完备化为基础, 定义了拓扑$k$-代数及其完备化, 并从射影极限的角度对完备化的进行了代数解释.
分类: 数学 >> 应用数学 提交时间: 2024-02-22
摘要: 本文研究Heisenberg群上非退化散度型次椭圆方程弱解的正则性。基于系数矩阵更一般的假设,本文针对齐次与非齐次两种情形,建立弱解在Besov空间中的水平Calderon-Zygmund估计。本文的研究将丰富发展Heisenberg群上非线性Calderon-Zygmund正则性理论。
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-18
摘要: Summary: In this paper we consider a variation of the classical Turn-type extremal problems. Let $S$be an $n$-term graphical sequence, and $\sigma(S)$be the sum of the terms in $S$. Let $H$be a graph. The problem is to determine the smallest even $l$such that any $n$-term graphical sequence $S$having $\sigma(S)\geq l$has a realization containing $H$as a subgraph. Denote this value $l$by $\sigma(H,n)$. We show $\sigma(C_{2m+1},n)=m(2n-m-1)+2$, for $m\geq 3$, $n\geq 3m$; $\sigma(C_{2m+2},n)=m(2n-m-1)+4$, for $m\geq 3$, $n\geq 5m-2$.''
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-18
摘要: In 1975, P. Erdős proposed the problem of determining the maximum number $f(n)$ of edges in a graph on $n$ vertices in which any two cycles are of different lengths. Let $f^{\ast}(n)$ be the maximum number of edges in a simple graph on $n$ vertices in which any two cycles are of different lengths. Let $M_n$ be the set of simple graphs on $n$ vertices in which any two cycles are of different lengths and with the edges of $f^{\ast}(n)$. Let $mc(n)$ be the maximum cycle length for all $G \in M_n$. In this paper, it is proved that for $n$ sufficiently large, $mc(n)\leq \frac{15}{16}n$. We make the following conjecture: $$\lim_{n \rightarrow \infty} {mc(n)\over n}= 0.$$
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-18
摘要: Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). We use the symbol $Z_4$ to denote $K_4-P_2.$ A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine the values of $\sigma (K_{r+1}-U, n)$ for $n\geq 5r+18, r+1 \geq k \geq 7,$ $j \geq 6$ where $U$ is a graph on $k$ vertices and $j$ edges which contains a graph $K_3 \bigcup P_3$ but not contains a cycle on 4 vertices and not contains $Z_4$. There are a number of graphs on $k$ vertices and $j$ edges which contains a graph $(K_{3} \bigcup P_{3})$ but not contains a cycle on 4 vertices and not contains $Z_4$. (for example, $C_3\bigcup C_{i_1} \bigcup C_{i_2} \bigcup >... \bigcup C_{i_p}$ $(i_j\neq 4, j=2,3,..., p, i_1 \geq 5)$, $C_3\bigcup P_{i_1} \bigcup P_{i_2} \bigcup ... \bigcup P_{i_p}$ $(i_1 \geq 3)$, $C_3\bigcup P_{i_1} \bigcup C_{i_2} \bigcup >... \bigcup C_{i_p}$ $(i_j\neq 4, j=2,3,..., p, i_1 \geq 3)$, etc)
分类: 数学 >> 数学(综合) 提交时间: 2024-02-17
摘要: 本文利用拉格朗日反演级数方法,研究了形如级数y=a1x+a2x2+a3x3++anxn+的在x=0的邻域内单调区间,然后针对更一般形式的级数方程,给出了其中一个非零实根的一个计算方法。
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-13
摘要: Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). We use the symbol $Z_4$ to denote $K_4-P_2.$ A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine the values of $\sigma (K_{r+1}-Z, n)$ for $n\geq 5r+19, r+1 \geq k \geq 5,$ $j \geq 5$ where $Z$ is a graph on $k$ vertices and $j$ edges which contains a graph $Z_4$ but not contains a cycle on $4$ vertices. We also determine the values of $\sigma (K_{r+1}-Z_4, n)$, $\sigma (K_{r+1}-(K_4-e), n)$, $\sigma (K_{r+1}-K_4, n)$ for $n\geq 5r+16, r\geq 4$.
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-13
摘要: Let $K_k$, $C_k$, $T_k$, and $P_{k}$ denote a complete graph on $k$ vertices, a cycle on $k$ vertices, a tree on $k+1$ vertices, and a path on $k+1$ vertices, respectively. Let $K_{m}-H$ be the graph obtained from $K_{m}$ by removing the edges set $E(H)$ of the graph $H$ ($H$ is a subgraph of $K_{m}$). A sequence $S$ is potentially $K_{m}-H$-graphical if it has a realization containing a $K_{m}-H$ as a subgraph. Let $\sigma(K_{m}-H, n)$ denote the smallest degree sum such that every $n$-term graphical sequence $S$ with $\sigma(S)\geq \sigma(K_{m}-H, n)$ is potentially $K_{m}-H$-graphical. In this paper, we determine the values of $\sigma (K_{r+1}-H, n)$ for $n\geq 4r+10, r\geq 3, r+1 \geq k \geq 4$ where $H$ is a graph on $k$ vertices which contains a tree on $4$ vertices but not contains a cycle on $3$ vertices. We also determine the values of $\sigma (K_{r+1}-P_2, n)$ for $n\geq 4r+8, r\geq 3$.
分类: 数学 >> 离散数学和组合数学 提交时间: 2024-02-10
摘要: A sequence $S$is potentially $K_4-e$graphical if it has a realization containing a $K_4-e$as a subgraph. Let $\sigma(K_4-e,n)$denote the smallest degree sum such that every $n$-term graphical sequence $S$with $\sigma(S)\geq\sigma(K_4-e,n)$is potentially $K_4-e$graphical. Gould, Jacobson, Lehel raised the problem of determining the value of $\sigma(K_4-e,n)$. In this paper, we prove that $\sigma(K_4-e,n)=2[(3n-1)/2]$for $n\geq7$and $n=4,5$, and $\sigma(K_4-e,6)=20$.''
分类: 数学 >> 统计和概率 提交时间: 2024-02-04
摘要: The three frameworks for theories of consciousness taken most 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 Entropypartition of complex system in present article. Human brains system self-organizably andadaptively implements partition 、 aggregation and integration, and consciousness emerges.The Gibss representation of consciousness is proved and That consciousness originates from quantum mechanical processes of brain activity is explained by means of SW entropy