https://netlify.sunisalex.org/写给好奇者的笔记。zh-CNhttps://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/07-trigonometric-functions/https://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/07-trigonometric-functions/Mon, 27 Jul 2026 12:00:00 GMT通过十五道典型例题梳理三角函数的恒等变形与综合应用，重点讲解和差化积、辅助角、万能公式、切化弦及对偶构造等解题方法。https://netlify.sunisalex.org/posts/technology/ocrbit/https://netlify.sunisalex.org/posts/technology/ocrbit/Mon, 27 Jul 2026 12:00:00 GMT从全局热键、多显示器截图、浏览器 Kiosk 框选，到 SSE 流式 OCR、科学公式提示词与 DPAPI 密钥保护，拆解 OCRBit 的轻量 Windows 架构。https://netlify.sunisalex.org/posts/chemistry/inorganic/manganese/https://netlify.sunisalex.org/posts/chemistry/inorganic/manganese/Sat, 25 Jul 2026 12:00:00 GMTAbstract 锰(Mn)位于 锰副族元素 ,后者位于$VIIB$族,包括锰(Mn),锝(Tc),铼(Re)和𬭛(Bh)四种过渡金属元素. 锰的成矿主要以 氧化物 形式出现: - 软锰矿$\ce{MnO2}$ - 黑锰矿$\ce{Mn3O4}$ - 方锰矿$\ce{MnO}$ - 菱锰矿$\ce{MnCO3}$https://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/02-AM-GM-inequalities/https://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/02-AM-GM-inequalities/Sat, 11 Jul 2026 12:00:00 GMT本文整理均值不等式的 22 道典型例题，涵盖分母换元、增量换元、配凑取等、局部不等式与乘积条件下的最值估计，适合强基计划和数学竞赛基础阶段系统复习。https://netlify.sunisalex.org/posts/chemistry/babychem/overview-of-stereochemistry/https://netlify.sunisalex.org/posts/chemistry/babychem/overview-of-stereochemistry/Fri, 10 Jul 2026 12:00:00 GMT本文介绍立体化学的基本研究对象，梳理分子的构成、构造、构型与构象之间的层级关系，并从键长、键角、中心原子杂化和孤对电子等方面整理分子共线与共面的基础判断方法。https://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/01-algebraic-manipulation/https://netlify.sunisalex.org/posts/math/2027-strong-foundation-plan/01-algebraic-manipulation/Fri, 10 Jul 2026 12:00:00 GMT本文围绕代数变形整理 15 道典型例题，涵盖恒等式、因式分解、对称式处理与常见变量代换，重点展示如何通过结构观察化繁为简，适合强基计划和数学竞赛基础阶段复习。https://netlify.sunisalex.org/posts/chemistry/babychem/alcohol-to-halide-conversion-and-alcohol-elimination/https://netlify.sunisalex.org/posts/chemistry/babychem/alcohol-to-halide-conversion-and-alcohol-elimination/Thu, 09 Jul 2026 12:00:00 GMT本文是【基础有机化学 L9-3 补充你的知识盲区，你真的理解醇的取代和消除反应吗？】的学习笔记https://netlify.sunisalex.org/posts/math/2022-labour-day/5-01-02/https://netlify.sunisalex.org/posts/math/2022-labour-day/5-01-02/Sun, 05 Jul 2026 12:00:00 GMT本文为培尖教育2022五一刷题班（5.1）的第二部分，继续通过典型例题讲解复数的共轭、模与复平面几何应用，包括实数判定、四点共圆、重心共圆及托勒密不等式；同时整理三角恒等变换、三倍角公式、三角函数最值与方程、复数换元解高次方程以及 Jensen 不等式等高联一试常用方法。https://netlify.sunisalex.org/posts/chemistry/babychem/basic-properties-of-alcohols/https://netlify.sunisalex.org/posts/chemistry/babychem/basic-properties-of-alcohols/Sat, 04 Jul 2026 12:00:00 GMT本文是【基础有机化学 L9-2 醇的基本性质，醇的酸碱性和亲核性，醇与无机酸的反应】 的笔记https://netlify.sunisalex.org/posts/chemistry/organic/perkin-reaction/https://netlify.sunisalex.org/posts/chemistry/organic/perkin-reaction/Sat, 04 Jul 2026 12:00:00 GMTPerkin 反应的机理、立体选择性、香豆素合成特例与分层练习。https://netlify.sunisalex.org/posts/math/2022-labour-day/5-01-01/https://netlify.sunisalex.org/posts/math/2022-labour-day/5-01-01/Sat, 27 Jun 2026 12:00:00 GMT本文为培尖教育2022五一刷题班（5.1）的复数专题复习笔记，系统梳理了复数的代数、三角、指数三种形式及几何应用（面积、共圆、相似），并通过10道典型例题详细演示了数形结合、旋转技巧、单位根求和及辐角主值处理等竞赛常用方法。https://netlify.sunisalex.org/posts/physics/celestial-movement/https://netlify.sunisalex.org/posts/physics/celestial-movement/Wed, 17 Jun 2026 12:00:00 GMT本文系统介绍了天体运动中的几个核心专题，包括拉格朗日点的求解与小量近似、双曲线与抛物线轨道问题、开普勒第一定律的微积分推导，以及若干典型习题的详细解答。https://netlify.sunisalex.org/posts/math/2022-labour-day/4-30-01/https://netlify.sunisalex.org/posts/math/2022-labour-day/4-30-01/Sun, 14 Jun 2026 12:00:00 GMT本讲义为2022年五一培尖刷题班（4.30）的高考数学专题，聚焦解析几何（抛物线、椭圆、圆）的综合应用与解题技巧。内容涵盖圆锥曲线与直线的位置关系、切线问题、轨迹方程、面积最值、定值定点证明等核心题型.题目来源包括历年自招、高考及竞赛改编题，难度层次分明，注重计算能力与几何直观的双重训练，适合拔高阶段学生系统突破解析几何难点。https://netlify.sunisalex.org/posts/physics/application-of-the-law-of-gravitation/https://netlify.sunisalex.org/posts/physics/application-of-the-law-of-gravitation/Mon, 08 Jun 2026 12:00:00 GMT以轨道力学为主线，依次讨论椭圆轨道的几何与物理性质、 抛物线轨道的面积速度法、三体稳定转动的拉格朗日解、 位力定理的一般形式及其在天体系统中的应用， 以及潮汐力的本质、洛希极限的推导与转动参考系下的卫星轨道变化。https://netlify.sunisalex.org/posts/physics/universal-law-of-graviation/https://netlify.sunisalex.org/posts/physics/universal-law-of-graviation/Sun, 07 Jun 2026 12:00:00 GMT万有引力定律全景:从开普勒三定律到三大宇宙速度,辅以球壳引力、双星三星、天体能量等专题与例题精解。https://netlify.sunisalex.org/posts/math/LYW-math-lessons-review/001/https://netlify.sunisalex.org/posts/math/LYW-math-lessons-review/001/Fri, 05 Jun 2026 12:00:00 GMThttps://netlify.sunisalex.org/posts/math/hypergeometric-distribution/https://netlify.sunisalex.org/posts/math/hypergeometric-distribution/Wed, 03 Jun 2026 12:00:00 GMT从定义出发,借助两条组合恒等式(降阶公式与范德蒙德恒等式)完整推导超几何分布的期望与方差,每一步都有据可循。https://netlify.sunisalex.org/posts/math/beijing-2025-haidian-final-exam-grade11/https://netlify.sunisalex.org/posts/math/beijing-2025-haidian-final-exam-grade11/Wed, 27 May 2026 12:00:00 GMT给定正整数$n(n\ge 3)$,若数列$A_n:a_1,a_2,...,a_n$同时满足下列两个性质，则称数列$A_n$为$P(n)$数列： 1. $\{a_1,a_2,..,a_n\}=\{1,2,...,n\}$ 2. 对任意$i\in\{1,2,...,n-2\}$,总存在$j\in\{i+1,i+2,...,n\}$，使得$|a_j-a_i|=2$https://netlify.sunisalex.org/posts/physics/basic-calculus-04/https://netlify.sunisalex.org/posts/physics/basic-calculus-04/Tue, 26 May 2026 12:00:00 GMT以微积分为工具求解物理问题：从机械能守恒、简谐运动与弹性势能，到曲率半径、虚功原理与变质量绳，再到微元法运动学与刚体转动惯量，串联力学中的微分方程与积分思想。https://netlify.sunisalex.org/posts/physics/basic-calculus-03/https://netlify.sunisalex.org/posts/physics/basic-calculus-03/Sun, 24 May 2026 12:00:00 GMT本文介绍微积分在物理中的应用，涵盖质心计算（圆锥、半球壳、半球体）、保守力势能与平衡稳定性判据、泰勒小量展开及其在电偶极子受力、相对论动能还原、非均匀浮力等经典问题中的应用。https://netlify.sunisalex.org/posts/physics/basic-calculus-02/https://netlify.sunisalex.org/posts/physics/basic-calculus-02/Fri, 22 May 2026 12:00:00 GMT从质量积分出发，系统介绍不定积分与定积分的概念、常用公式及换元法，并通过重心计算、n维球体积推导、阻力运动等物理例题，展示积分在竞赛物理中的实际应用。https://netlify.sunisalex.org/posts/physics/basic-calculus-01/https://netlify.sunisalex.org/posts/physics/basic-calculus-01/Sun, 17 May 2026 12:00:00 GMT本文中涉及到的微积分服务于 物理竞赛 ,侧重于 实用性 ,而非 严谨性https://netlify.sunisalex.org/posts/math/focal-chord-length-formula/https://netlify.sunisalex.org/posts/math/focal-chord-length-formula/Sun, 10 May 2026 12:00:00 GMT圆锥曲线的焦点弦长是题目常常设问之处,本文用 直线参数方程 推导了: - 椭圆 - 双曲线 - 抛物线 的 焦点弦长公式https://netlify.sunisalex.org/posts/math/AM-GM-inequality-01/https://netlify.sunisalex.org/posts/math/AM-GM-inequality-01/Tue, 05 May 2026 12:00:00 GMT小蓝本《均值不等式与柯西不等式》第一章课后习题(个人解答)https://netlify.sunisalex.org/posts/android/PJX110-crdroid/https://netlify.sunisalex.org/posts/android/PJX110-crdroid/Sun, 03 May 2026 12:00:00 GMT[!WARNING] 以下教程仅供 一加Ace3Pro 安装crDroid 12(corvette)使用 玩机不规范,亲人两行泪 由操作不当造成的硬件损坏,请读者自负!https://netlify.sunisalex.org/posts/math/max-minus-min-sequence/https://netlify.sunisalex.org/posts/math/max-minus-min-sequence/Sun, 26 Apr 2026 12:00:00 GMT第(I)问枚举 $a_4$ 的可能值；第(II)问证明若有最大值则必含 $0$；第(III)问用反证法证明正项数列无上界：假设存在上界 $M$，可导出相邻一大一小两项，递推三步后大项增加 $2\\times$ 小项，不断重复终将超过 $M$，矛盾。https://netlify.sunisalex.org/posts/math/hermite-hadamard-inequality/https://netlify.sunisalex.org/posts/math/hermite-hadamard-inequality/Sat, 25 Apr 2026 12:00:00 GMThttps://netlify.sunisalex.org/posts/chemistry/competition/2026-beijing-preliminary/https://netlify.sunisalex.org/posts/chemistry/competition/2026-beijing-preliminary/Sun, 19 Apr 2026 12:00:00 GMT2026 年高中化学奥林匹克北京地区预选赛,没有难绷的元素推断,全是 化学基本理论 的运用与 热力学计算 .https://netlify.sunisalex.org/posts/chemistry/competition/2026-summar-vacation-7-12/https://netlify.sunisalex.org/posts/chemistry/competition/2026-summar-vacation-7-12/Sun, 19 Apr 2026 12:00:00 GMT储氢技术(39届) 6.1 高压储氢。压缩氢气是目前最常用的储氢方法之一。氢气被存储在压力维持在 350 700 bar 的容器中，高压下其行为偏离理想气体，更适合用范德华方程$(p + a/V_{\text{m}}^2)(V_{\text{m}} - b) = RT$描述，其中 $V_{\text{m}}$ 为气体的摩尔体积，$p$ 为气体压强。对氢气而言，方程中的 $a = 0.02476\ \text{J}\cdot\text{m}^3\cdot\text{mol}^{-2}$https://netlify.sunisalex.org/posts/math/arithmetic-geometric-sequence-lambda/https://netlify.sunisalex.org/posts/math/arithmetic-geometric-sequence-lambda/Sat, 18 Apr 2026 12:00:00 GMT引入 已知$\{a_n\}$是首项为$a$,公差为2的无限等差数列,$\{b_n\}$是首项为1,公比为2的无限等比数列,记$\lambda_n = \dfrac{a_1 + a_2 + \cdots + a_n}{b_n}$,给出下列四个结论：https://netlify.sunisalex.org/posts/math/sequence-transform-t1-t2/https://netlify.sunisalex.org/posts/math/sequence-transform-t1-t2/Sat, 18 Apr 2026 12:00:00 GMT（2024·徐州模拟）对于每项均是正整数的数列 $P:a_1,a_2,\cdots,a_n$，定义变换 $T_1$，$T_1$ 将数列 $P$ 变换成数列 $T_1(P):n,a_1-1,a_2-1,\cdots,a_n-1$。对于每项均是非负整数的数列 $Q:b_1,b_2,\cdots,b_m$，定义 $S(Q)=2(b_1+2b_2+\cdots+mb_m)+b_1^2+b_2^2+\cdots+b_m^2$https://netlify.sunisalex.org/posts/math/factor-a3-b3-c3-3abc/https://netlify.sunisalex.org/posts/math/factor-a3-b3-c3-3abc/Sat, 11 Apr 2026 12:00:00 GMT详细推导 a^3 + b^3 + c^3 - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca) 的因式分解及应用