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 >> 计算数学 提交时间: 2024-01-04
摘要: This paper presents error analysis of stabilizer free weak Galerkin finite element method (SFWG-FEM) for a second order elliptic equation with low regularity solutions. The standard error analysis of SFWG-FEM requires additional regularity on solutions, such as $H^2$-regularity for the second-order convergence. However, if the solutions are in $H^{1+s}$ with $0< s < 1$, numerical experiments show that the SFWG-FEM is also effective and stable with the $(1+s)$-order convergence rate, so we develop a theoretical analysis for it. We introduce a standard $H^{2}$ finite element approximation for the elliptic problem, and then we apply the SFWG-FEM to approach this smooth approximating finite element solution. Finally, we establish the error analysis for SFWG-FEM with low regularity in both discrete $H^1$-norm and standard $L^2$-norm. The ($P_{k}(T),P_{k-1}(e), P_{k+1}(T) ^d$) elements with dimensions of space $d = 2,3$ are employed and the numerical examples are tested to confirm the theory.
分类: 数学 >> 计算数学 提交时间: 2023-12-25
摘要: This paper introduces a new kind of multigrid approach for semilinear elliptic problems, which is based on the symmetric interior penalty discontinuous Galerkin (SIPDG) method. We first give an optimal error estimate of the SIPDG method for the problem. Then, we design a type of multigrid method, which is called the multilevel correction method, and derive a-priori error estimates. The primary idea of this method is to take the solution of the semilinear problem and utilize it to establish a sequence of solutions for associated linear boundary value problem on discontinuous finite element spaces and a newly defined low dimensional augmented subspace. Lastly, numerical experiments are offered to confirm the suggested method's precision and effectiveness.
分类: 数学 >> 代数与数论 分类: 数学 >> 离散数学和组合数学 提交时间: 2023-12-04
摘要: 令An是 2 次Jacobson根为零的A型Nakayama代数, Xn 是 2 次Jacobson根为零的 tilde{A}型Nakayama代数. 本文考虑了An与Xn的k-张量An tensor Xn上的不可分解模的分类问题, 并给出其在同构意义下的计数公式.
分类: 统计学 >> 应用统计数学 分类: 计算机科学 >> 计算机应用技术 分类: 数学 >> 建模与仿真 分类: 能源科学 >> 能源(综合) 提交时间: 2024-01-01
摘要: The surging demand for new energy vehicles is propelled by the call to conserve energy, curtail emissions, and enhance the ecological ambience. By conducting behavioral analysis and mining, particular usage patterns of new en#2;ergy vehicles are pinpointed. Regrettably, these models decrease their environ#2;mental shielding efficiency. For instance, overloading the battery, operating with low battery power, and driving at excessive speeds can all detrimentally affect the battery's performance. To assess the impact of such driving behavior on the urban ecology, an environmental computational modeling method has been pro#2;posed to simulate the interaction between new energy vehicles and the environ#2;ment. To extend the time series data of the vehicle's entire life cycle and the eco#2;logical environment within the model sequence data, I utilized the LSTM deep learning method with Bayesian optimizer optimization parameters for longer simulation. The analysis revealed the detrimental effects of poor driving behavior on the environment
分类: 数学 >> 控制和优化 提交时间: 2023-12-04
摘要: In this paper, we mainly dicuss the analytic conditions of copositivity of a class of 4th order 3-dimensional symmetric tensors. For a 4th order 3-dimensional symmetric tensor with its entries $1$ or $-1$, an analytic necessary and sufficient condition is given for its strict copositivity with the help of the properties of strictly semi-positive tensors. And by means of usual maxi-min theory, a necessary and sufficient condition is established for copositivity of such a tensor also. Applying these conclusions to a general 4th order 3-dimensional symmetric tensor, the analytic conditions are successfully obtained for verifying the (strict) copositivity, and these conditions can be very easily parsed and validated.
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 >> 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 >> 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 >> 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: 2024-02-18
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: 2024-03-01
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 >> 代数与数论 提交时间: 2022-08-07
摘要: 胞腔代数是近年来备受关注的一种代数结构,而分次代数在表示论之中起着非常重要的作用。基于王涛对预胞腔代数的研究,给出分次预胞腔代数的定义,并且讨论了分次预胞腔代数的表示理论,最后还研究了正则半群代数的分次预胞腔性。
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 >> 代数与数论 提交时间: 2022-08-07
摘要: 胞腔代数是近年来备受关注的一种代数结构,而正则半群是一类重要的半群,是半群代数理论的主要研究领域之一。基于Du和Rui所提出的一类广义胞腔代数标准基代数,对正则半群代数的广义胞腔性进行了研究。
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 >> 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: 2024-03-27
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 >> 数学(综合) 提交时间: 2018-09-22
摘要: We establish regularity of solutions to the $G$-Laplace equation $-\text{div}\ \bigg(\frac{g(|\nabla u|)}{|\nabla u|}\nabla u\bigg)=\mu$, where $\mu$ is a nonnegative Radon measure satisfying $\mu (B_{r}(x_{0}))\leq Cr^{m}$ for any ball $B_{r}(x_{0})\subset\subset \Omega$ with $r\leq 1$ and $m>n-1-\delta\geq 0$. The function $g(t)$ is supposed to be nonnegative and $C^{1}$-continuous in $[0,+\infty)$, satisfying $g(0)=0$, and for some positive constants $\delta$ and $g_{0}$, $\delta\leq \frac{tg'(t)}{g(t)}\leq g_{0}, \forall t>0$, that generalizes the structural conditions of Ladyzhenskaya-Ural'tseva for an elliptic operator.
分类: 动力与电气工程 >> 电气工程 分类: 数学 >> 控制和优化 提交时间: 2022-08-07
摘要: 本文研究含随机风电的机组组合问题, 基于分布鲁棒优化提出了考虑风功率预测的条件误差和误差时空相关性的建模及优化方法. 首先, 为了量化计算风功率的预测误差, 用Lasso(最小绝对值收敛和选择算子)训练得到鲁棒的条件误差估计器;为了获取风功率预测误差的时空关联信息, 通过无偏估计从历史数据得到误差的协方差矩阵. 用所得的条件误差和协方差矩阵构造了改进的风功率预测误差的概率分布模糊集. 其次, 在多面体支撑集上建立了风功率预测误差的随机量, 构建了两阶段分布鲁棒机组组合模型, 并提出了与该模型等效的混合整数半正定规划模型. 再次, 提出了从第二阶段半正定优化问题辨识极限分布的方法, 并提出了利用极限分布求解两阶段分布鲁棒机组组合问题的高效割平面算法. 最后, 进行数值实验, 验证了所提模型在应对风功率预测误差的时空关联性方面的能力和优势, 验证了模型决策方案的经济性和鲁棒性.