{
  "version": "https://jsonfeed.org/version/1.1",
  "title": "nan2inf.cn",
  "home_page_url": "https://nan2inf.cn/",
  "feed_url": "https://nan2inf.cn/feed.json",
  "description": "个人写作、研究笔记、数学、算法、项目和小工具。",
  "language": "zh-CN",
  "authors": [
    {
      "name": "nan2inf",
      "url": "https://nan2inf.cn/"
    }
  ],
  "items": [
    {
      "id": "https://nan2inf.cn/math/abstract-algebra-course-map/",
      "url": "https://nan2inf.cn/math/abstract-algebra-course-map/",
      "title": "抽象代数学习路线",
      "summary": "围绕群、环、域与模组织抽象代数笔记，并给出适合连续阅读的入口。",
      "content_text": "围绕群、环、域与模组织抽象代数笔记，并给出适合连续阅读的入口。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "数学",
        "数学",
        "抽象代数",
        "学习路线"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/group-action-orbit-stabilizer/",
      "url": "https://nan2inf.cn/math/group-action-orbit-stabilizer/",
      "title": "群作用与轨道-稳定子定理",
      "summary": "从群作用出发整理轨道、稳定子、类方程与 Burnside 引理之间的关系。",
      "content_text": "从群作用出发整理轨道、稳定子、类方程与 Burnside 引理之间的关系。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "数学",
        "math",
        "abstract-algebra",
        "group-action"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/first-order-characteristics/",
      "url": "https://nan2inf.cn/math/first-order-characteristics/",
      "title": "一阶线性方程的特征线解法",
      "summary": "用特征线方法求解一阶线性偏微分方程，并整理初值条件的处理过程。",
      "content_text": "用特征线方法求解一阶线性偏微分方程，并整理初值条件的处理过程。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "数学",
        "math",
        "pde"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/hahn-banach-theorem/",
      "url": "https://nan2inf.cn/math/hahn-banach-theorem/",
      "title": "Hahn-Banach 定理",
      "summary": "Hahn-Banach 定理的实形式、复形式及其在线性泛函延拓中的作用。",
      "content_text": "Hahn-Banach 定理的实形式、复形式及其在线性泛函延拓中的作用。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "数学",
        "math",
        "functional-analysis"
      ]
    },
    {
      "id": "https://nan2inf.cn/algo/nowcoder-2024-summer-camp-10/",
      "url": "https://nan2inf.cn/algo/nowcoder-2024-summer-camp-10/",
      "title": "2024 暑期牛客多校训练营 10",
      "summary": "2024 暑期牛客多校训练营第十场题解，记录建模、推导与 C++ 实现。",
      "content_text": "2024 暑期牛客多校训练营第十场题解，记录建模、推导与 C++ 实现。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "算法",
        "algo",
        "contest",
        "nowcoder",
        "code"
      ]
    },
    {
      "id": "https://nan2inf.cn/algo/linear-list-adt-implementation/",
      "url": "https://nan2inf.cn/algo/linear-list-adt-implementation/",
      "title": "线性表 ADT 的实现",
      "summary": "线性表抽象数据类型的顺序与链式实现，包含 C++ 接口、复杂度和边界处理。",
      "content_text": "线性表抽象数据类型的顺序与链式实现，包含 C++ 接口、复杂度和边界处理。",
      "date_published": "2026-06-01T00:00:00.000Z",
      "date_modified": "2026-06-01T00:00:00.000Z",
      "tags": [
        "算法",
        "algo",
        "data-structures"
      ]
    },
    {
      "id": "https://nan2inf.cn/blog/static-first-personal-site/",
      "url": "https://nan2inf.cn/blog/static-first-personal-site/",
      "title": "静态优先的个人站",
      "summary": "为什么 nan2inf.cn 从静态页面和小后端面开始。",
      "content_text": "为什么 nan2inf.cn 从静态页面和小后端面开始。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "博客",
        "architecture",
        "astro",
        "deployment"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/pulse-graph-interface/",
      "url": "https://nan2inf.cn/research/pulse-graph-interface/",
      "title": "脉冲图界面笔记",
      "summary": "一种不依赖重型 WebGL 的技术页面轻量视觉语言。",
      "content_text": "一种不依赖重型 WebGL 的技术页面轻量视觉语言。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "研究",
        "interface",
        "canvas",
        "research"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/compact-proof-patterns/",
      "url": "https://nan2inf.cn/math/compact-proof-patterns/",
      "title": "紧凑证明模式",
      "summary": "一则关于如何在 MDX 中保持定义、命题和证明草图可读的小笔记。",
      "content_text": "一则关于如何在 MDX 中保持定义、命题和证明草图可读的小笔记。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "数学",
        "proof",
        "mdx",
        "notes"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy-formula-rendering/",
      "url": "https://nan2inf.cn/math/legacy-formula-rendering/",
      "title": "TeX 公式的网页排版约定",
      "summary": "记录行内公式、行间公式与兼容写法在网页阅读中的排版边界。",
      "content_text": "记录行内公式、行间公式与兼容写法在网页阅读中的排版边界。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "数学",
        "数学",
        "TeX",
        "KaTeX"
      ]
    },
    {
      "id": "https://nan2inf.cn/algo/queue-boundaries/",
      "url": "https://nan2inf.cn/algo/queue-boundaries/",
      "title": "小系统里的队列边界",
      "summary": "一则关于为什么个人工具后端的后台任务应当基于白名单的小笔记。",
      "content_text": "一则关于为什么个人工具后端的后台任务应当基于白名单的小笔记。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "算法",
        "rq",
        "security",
        "backend"
      ]
    },
    {
      "id": "https://nan2inf.cn/projects/ascend-archive/",
      "url": "https://nan2inf.cn/projects/ascend-archive/",
      "title": "Ascend 竞赛资料索引",
      "summary": "整理 Ascend 竞赛、性能优化与榜单系统中值得长期保留的实现记录。",
      "content_text": "整理 Ascend 竞赛、性能优化与榜单系统中值得长期保留的实现记录。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "项目",
        "Ascend",
        "竞赛",
        "性能优化"
      ]
    },
    {
      "id": "https://nan2inf.cn/projects/personal-site/",
      "url": "https://nan2inf.cn/projects/personal-site/",
      "title": "nan2inf.cn 个人站",
      "summary": "以 Astro 静态内容为主体、Django 小后端为补充的个人知识站。",
      "content_text": "以 Astro 静态内容为主体、Django 小后端为补充的个人知识站。",
      "date_published": "2026-05-31T00:00:00.000Z",
      "date_modified": "2026-05-31T00:00:00.000Z",
      "tags": [
        "项目",
        "astro",
        "django",
        "infra"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-262/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-262/",
      "title": "23年",
      "summary": "语言模型的重要意义，有哪些语言模型 unigram bigram计算。",
      "content_text": "语言模型的重要意义，有哪些语言模型 unigram bigram计算。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-263/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-263/",
      "title": "24年",
      "summary": "一、简答（40’，每个8’） 1. HMM和BMM方法的定义，以及两者的主要区别。",
      "content_text": "一、简答（40’，每个8’） 1. HMM和BMM方法的定义，以及两者的主要区别。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-264/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-264/",
      "title": "25年",
      "summary": "语言模型是什么？有什么常见的语言模型？ 简单计算 unigram, bigram。",
      "content_text": "语言模型是什么？有什么常见的语言模型？ 简单计算 unigram, bigram。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-273/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-273/",
      "title": "词法",
      "summary": "Bi-directional MM: 双向最大匹配算法。",
      "content_text": "Bi-directional MM: 双向最大匹配算法。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-272/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-272/",
      "title": "词义",
      "summary": "NLP中关于「词义」的主题笔记。",
      "content_text": "NLP中关于「词义」的主题笔记。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-271/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-271/",
      "title": "机器翻译",
      "summary": "NLP中关于「机器翻译」的主题笔记。",
      "content_text": "NLP中关于「机器翻译」的主题笔记。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-course-613/",
      "url": "https://nan2inf.cn/research/legacy/com-course-613/",
      "title": "计算机视觉",
      "summary": "计算机视觉的课程笔记，按主题、章节与习题整理。",
      "content_text": "计算机视觉的课程笔记，按主题、章节与习题整理。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-12T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-627/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-627/",
      "title": "计算机视觉期末复习笔记",
      "summary": "系统整理图像滤波、特征提取、分割、几何与深度学习等计算机视觉核心主题。",
      "content_text": "系统整理图像滤波、特征提取、分割、几何与深度学习等计算机视觉核心主题。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "图像处理",
        "深度学习",
        "复习笔记"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-622/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-622/",
      "title": "计算机视觉实验 1：卷积与二维图像处理",
      "summary": "围绕二维卷积、互相关和滤波复杂度展开的理论推导与图像处理实验。",
      "content_text": "围绕二维卷积、互相关和滤波复杂度展开的理论推导与图像处理实验。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "二维卷积",
        "互相关",
        "实验"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-268/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-268/",
      "title": "句法",
      "summary": "Inside-Outside（内外）算法的问题 计算速度慢 每次迭代的时间复杂度为 ，其中 ， 表示文法中非终结符的数量。 容易陷入局部最优 Charniak 指出，在每一次试验中，算法往往会收敛到不同的局部最大值。",
      "content_text": "Inside-Outside（内外）算法的问题 计算速度慢 每次迭代的时间复杂度为 ，其中 ， 表示文法中非终结符的数量。 容易陷入局部最优 Charniak 指出，在每一次试验中，算法往往会收敛到不同的局部最大值。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-267/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-267/",
      "title": "句义分析概览",
      "summary": "自然语言处理中的格语法与语义角色标注主题索引。",
      "content_text": "自然语言处理中的格语法与语义角色标注主题索引。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "句义分析",
        "语义角色标注"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-270/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-270/",
      "title": "期末",
      "summary": "{pages/NLP/23年} {pages/NLP/24年} {pages/NLP/25年}。",
      "content_text": "{pages/NLP/23年} {pages/NLP/24年} {pages/NLP/25年}。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-265/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-265/",
      "title": "人机交互",
      "summary": "面向任务的人机交互, 大概由什么样的内容组合 (1) 人际交流是人类社会的一个主要特征, 是推动人类社会向前发展的重要动力 (2) 自然语言是人际交流的主要工具之一 (3) 对话是使用自然语言进行人际交流的主要方式之一。",
      "content_text": "面向任务的人机交互, 大概由什么样的内容组合 (1) 人际交流是人类社会的一个主要特征, 是推动人类社会向前发展的重要动力 (2) 自然语言是人际交流的主要工具之一 (3) 对话是使用自然语言进行人际交流的主要方式之一。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-course-518/",
      "url": "https://nan2inf.cn/research/legacy/com-course-518/",
      "title": "昇腾开发板",
      "summary": "昇腾开发板的课程笔记，按主题、章节与习题整理。",
      "content_text": "昇腾开发板的课程笔记，按主题、章节与习题整理。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-12T00:00:00.000Z",
      "tags": [
        "研究",
        "昇腾开发板"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-624/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-624/",
      "title": "实验2-1 图像变换",
      "summary": "1. 掌握图像的参数化几何变换原理 2. 掌握图像的前向变换与逆向变换 3. 掌握图像的下抽样原理以及图像的内插方法原理 4. 掌握图像的高斯金字塔与拉普拉斯金字塔表示原理 前向变换: ; 存在问题 不一定是整数 逆向变换: ; 存在问题 不一定可逆. 且逆变换也不一定是整数。",
      "content_text": "1. 掌握图像的参数化几何变换原理 2. 掌握图像的前向变换与逆向变换 3. 掌握图像的下抽样原理以及图像的内插方法原理 4. 掌握图像的高斯金字塔与拉普拉斯金字塔表示原理 前向变换: ; 存在问题 不一定是整数 逆向变换: ; 存在问题 不一定可逆. 且逆变换也不一定是整数。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "实验报告",
        "实验"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-623/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-623/",
      "title": "实验2-2 特征检测",
      "summary": "1. 计算基于高斯一阶微分的图像梯度（幅值图与方向图）, 分析高斯方差对图像梯度的影响。",
      "content_text": "1. 计算基于高斯一阶微分的图像梯度（幅值图与方向图）, 分析高斯方差对图像梯度的影响。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "实验报告",
        "实验"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-625/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-625/",
      "title": "实验3 相机标定实验",
      "summary": "软件: 华谷动力相机驱动, python (环境如下)。",
      "content_text": "软件: 华谷动力相机驱动, python (环境如下)。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "实验报告",
        "实验"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-626/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-626/",
      "title": "实验5 目标检测",
      "summary": "以 的检测窗口为例, cell 大小为 , block 为 , 则窗口内 HOG 特征维度为。",
      "content_text": "以 的检测窗口为例, cell 大小为 , block 为 , 则窗口内 HOG 特征维度为。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "实验报告",
        "实验"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-619/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-619/",
      "title": "图像滤波：信号、卷积与边缘",
      "summary": "从离散信号与卷积出发，整理图像平滑、差分算子和边缘检测的基本方法。",
      "content_text": "从离散信号与卷积出发，整理图像平滑、差分算子和边缘检测的基本方法。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "图像滤波",
        "卷积",
        "边缘检测"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-269/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-269/",
      "title": "文本分类",
      "summary": "NLP中关于「文本分类」的主题笔记。",
      "content_text": "NLP中关于「文本分类」的主题笔记。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-266/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-266/",
      "title": "信息检索",
      "summary": "NLP中关于「信息检索」的主题笔记。",
      "content_text": "NLP中关于「信息检索」的主题笔记。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-274/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-274/",
      "title": "语言模型",
      "summary": "目标: 给定词串 , 计算概率 , 表示这个词序列在自然语言中出现的概率 (合理性)。",
      "content_text": "目标: 给定词串 , 计算概率 , 表示这个词序列在自然语言中出现的概率 (合理性)。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-knowledge-620/",
      "url": "https://nan2inf.cn/research/legacy/com-knowledge-620/",
      "title": "ImageTransformation",
      "summary": "几何变换 为什么需要缩放? 远处的物体看起来小，近处的物体看起来大 需要识别不同尺度的物体（尺度不变性） 将图像调整到相同大小有助于识别。",
      "content_text": "几何变换 为什么需要缩放? 远处的物体看起来小，近处的物体看起来大 需要识别不同尺度的物体（尺度不变性） 将图像调整到相同大小有助于识别。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "研究",
        "计算机视觉",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/research/legacy/com-course-256/",
      "url": "https://nan2inf.cn/research/legacy/com-course-256/",
      "title": "NLP",
      "summary": "NLP的课程笔记，按主题、章节与习题整理。",
      "content_text": "NLP的课程笔记，按主题、章节与习题整理。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-12T00:00:00.000Z",
      "tags": [
        "研究",
        "NLP"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-474/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-474/",
      "title": "\\fly 分析初步",
      "summary": "对任意的 以及 , 令 则在上述运算下 是 上的线性空间, 从而 有一个基 对于复值函数 . 若 均在 上可积, 则定义。",
      "content_text": "对任意的 以及 , 令 则在上述运算下 是 上的线性空间, 从而 有一个基 对于复值函数 . 若 均在 上可积, 则定义。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "数学分析",
        "资料"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-291/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-291/",
      "title": "1",
      "summary": "试证明圆锥形杆的微小纵振动方程是 其中 是圆锥的高, 分别是它的密度与杨氏模量, 且 为常数。",
      "content_text": "试证明圆锥形杆的微小纵振动方程是 其中 是圆锥的高, 分别是它的密度与杨氏模量, 且 为常数。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "偏微分方程",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-366/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-366/",
      "title": "1",
      "summary": "1. 求下列复数 的模 与辐角的主值 (1) (2)。",
      "content_text": "1. 求下列复数 的模 与辐角的主值 (1) (2)。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "复变函数",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-372/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-372/",
      "title": "1",
      "summary": "复数及其运算, 共轭复数, 复数的模等定义与高中相同。",
      "content_text": "复数及其运算, 共轭复数, 复数的模等定义与高中相同。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "复变函数",
        "复平面拓扑"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-393/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-393/",
      "title": "1",
      "summary": "P11/1: 试证明: 设 以及 都是定义在 上的实值函数, 且有 则对 , 有。",
      "content_text": "P11/1: 试证明: 设 以及 都是定义在 上的实值函数, 且有 则对 , 有。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "实变函数",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-463/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-463/",
      "title": "1",
      "summary": "1、已知准确值 , 则近似值: 有\\\\\\\\位有效数字, 有\\\\\\\\位有效数字。",
      "content_text": "1、已知准确值 , 则近似值: 有\\\\\\\\位有效数字, 有\\\\\\\\位有效数字。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "数值分析",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-531/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-531/",
      "title": "1",
      "summary": "10. 若 为随机事件, 说明下列各关系式的概率意义。",
      "content_text": "10. 若 为随机事件, 说明下列各关系式的概率意义。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "概率论",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-635/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-635/",
      "title": "1",
      "summary": "使用单纯形法来求解如下优化问题： 要求： 将其转化为标准形式，列出单纯形表手算作答。",
      "content_text": "使用单纯形法来求解如下优化问题： 要求： 将其转化为标准形式，列出单纯形表手算作答。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "运筹学",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-328/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-328/",
      "title": "1.1",
      "summary": "确定 Petersen 图的独立数 (independent number, 最大独立集的大小)、团数 (clique number, 最大团的大小) 和染色数。",
      "content_text": "确定 Petersen 图的独立数 (independent number, 最大独立集的大小)、团数 (clique number, 最大团的大小) 和染色数。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "图论与组合",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-329/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-329/",
      "title": "1.2",
      "summary": "确定下列命题的真假 a) 任意非连通图都有一个孤立顶点 b) 一个图是连通的当且仅当它的某个顶点与其他所有顶点是连通的 c) 任意闭合迹的边集可以划分成若干个环的边集 d) 如果图中有一个极大迹不是闭合的, 则其端点的度是奇数。",
      "content_text": "确定下列命题的真假 a) 任意非连通图都有一个孤立顶点 b) 一个图是连通的当且仅当它的某个顶点与其他所有顶点是连通的 c) 任意闭合迹的边集可以划分成若干个环的边集 d) 如果图中有一个极大迹不是闭合的, 则其端点的度是奇数。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "图论与组合",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-330/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-330/",
      "title": "1.3",
      "summary": "证明或证伪: 如果 是仅有的两个度数为奇数的点, 那么存在一条 -path。",
      "content_text": "证明或证伪: 如果 是仅有的两个度数为奇数的点, 那么存在一条 -path。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "图论与组合",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-331/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-331/",
      "title": "1.4",
      "summary": "证明: 存在一个 -顶点的竞赛图使得其中每个顶点的入度等于出度当且仅当 是奇数。",
      "content_text": "证明: 存在一个 -顶点的竞赛图使得其中每个顶点的入度等于出度当且仅当 是奇数。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "图论与组合",
        "作业",
        "习题"
      ]
    },
    {
      "id": "https://nan2inf.cn/math/legacy/com-knowledge-394/",
      "url": "https://nan2inf.cn/math/legacy/com-knowledge-394/",
      "title": "10",
      "summary": "P218/8: 试证明 当且仅当存在 上的递增函数 , 使得。",
      "content_text": "P218/8: 试证明 当且仅当存在 上的递增函数 , 使得。",
      "date_published": "2026-02-12T00:00:00.000Z",
      "date_modified": "2026-02-13T00:00:00.000Z",
      "tags": [
        "数学",
        "exam",
        "实变函数",
        "作业",
        "习题"
      ]
    }
  ]
}