https://next.sunisalex.org/en/Notes for curious people.enhttps://next.sunisalex.org/en/posts/technology/ocrbit/https://next.sunisalex.org/en/posts/technology/ocrbit/Mon, 27 Jul 2026 12:00:00 GMTA technical tour of OCRBit's lightweight Windows architecture, from global hotkeys and multi-monitor capture to browser-based selection, SSE streaming, formula-aware prompts, and DPAPI-protected credentials.https://next.sunisalex.org/en/posts/chemistry/inorganic/manganese/https://next.sunisalex.org/en/posts/chemistry/inorganic/manganese/Sat, 25 Jul 2026 12:00:00 GMTA systematic overview of manganese chemistry, from the element and its coordination compounds to manganates, permanganates, laboratory reactions, and analytical applications.https://next.sunisalex.org/en/posts/math/2027-strong-foundation-plan/02-AM-GM-inequalities/https://next.sunisalex.org/en/posts/math/2027-strong-foundation-plan/02-AM-GM-inequalities/Sat, 11 Jul 2026 12:00:00 GMTThis article compiles 22 typical examples of mean inequality, covering denominator substitution, incremental substitution, matching, etc., local inequalities and the best estimate under product conditions. It is suitable for systematic review of the strong foundation plan and the basic stage of mathematics competitions.https://next.sunisalex.org/en/posts/chemistry/babychem/overview-of-stereochemistry/https://next.sunisalex.org/en/posts/chemistry/babychem/overview-of-stereochemistry/Fri, 10 Jul 2026 12:00:00 GMTThis article introduces the basic research objects of stereochemistry, sorting out the hierarchical relationship between the composition, structure, configuration and conformation of molecules, and sorting out the basic judgment methods of molecular collinearity and coplanarity from the aspects of bond length, bond angle, central atom hybridization and lone pair of electrons.https://next.sunisalex.org/en/posts/math/2027-strong-foundation-plan/01-algebraic-manipulation/https://next.sunisalex.org/en/posts/math/2027-strong-foundation-plan/01-algebraic-manipulation/Fri, 10 Jul 2026 12:00:00 GMTThis article organizes 15 typical example questions around algebraic deformation, covering identities, factorization, symmetry processing and common variable substitutions. It focuses on showing how to simplify the complex through structural observation. It is suitable for the review of the strong foundation plan and the basic stage of mathematics competitions.https://next.sunisalex.org/en/posts/chemistry/babychem/alcohol-to-halide-conversion-and-alcohol-elimination/https://next.sunisalex.org/en/posts/chemistry/babychem/alcohol-to-halide-conversion-and-alcohol-elimination/Thu, 09 Jul 2026 12:00:00 GMTThese are study notes for Basic Organic Chemistry L9-3: Do You Really Understand Substitution and Elimination Reactions of Alcohols?.https://next.sunisalex.org/en/posts/math/2022-labour-day/5-01-02/https://next.sunisalex.org/en/posts/math/2022-labour-day/5-01-02/Sun, 05 Jul 2026 12:00:00 GMTThis article is the second part of Peijian Education's 2022 May 1st question brushing class (5.1). It continues to explain the conjugate, module and complex plane geometry applications of complex numbers through typical examples, including real number determination, four-point concircle, barycentric concircle and Ptolemy's inequality; at the same time, it organizes common methods for high-level joint test such as trigonometric identity transformation, triple angle formula, trigonometric function minimum and equation, complex number replacement to solve higher-order equations and Jensen's inequality.https://next.sunisalex.org/en/posts/chemistry/babychem/basic-properties-of-alcohols/https://next.sunisalex.org/en/posts/chemistry/babychem/basic-properties-of-alcohols/Sat, 04 Jul 2026 12:00:00 GMTThese are study notes for Basic Organic Chemistry L9-2: Properties, Acid–Base Behavior, and Nucleophilicity of Alcohols.https://next.sunisalex.org/en/posts/chemistry/organic/perkin-reaction/https://next.sunisalex.org/en/posts/chemistry/organic/perkin-reaction/Sat, 04 Jul 2026 12:00:00 GMTPerkin reaction mechanism, stereoselectivity, special cases of coumarin synthesis and layering exercises.https://next.sunisalex.org/en/posts/math/2022-labour-day/5-01-01/https://next.sunisalex.org/en/posts/math/2022-labour-day/5-01-01/Sat, 27 Jun 2026 12:00:00 GMTThis article is the review notes for complex numbers in Peijian Education's 2022 May 1st question brushing class (5.1). It systematically sorts out the three forms of complex numbers, algebra, trigonometric, and exponent, as well as geometric applications (area, cocircle, similarity), and demonstrates in detail the combination of numbers and shapes, rotation skills, unit root summation, and argument principal value processing through 10 typical example questions.https://next.sunisalex.org/en/posts/physics/celestial-movement/https://next.sunisalex.org/en/posts/physics/celestial-movement/Wed, 17 Jun 2026 12:00:00 GMTThis article systematically introduces several core topics in celestial motion, including the solution and small quantity approximation of Lagrangian points, hyperbola and parabolic orbit problems, calculus derivation of Kepler's first law, and detailed answers to several typical exercises.https://next.sunisalex.org/en/posts/math/2022-labour-day/4-30-01/https://next.sunisalex.org/en/posts/math/2022-labour-day/4-30-01/Sun, 14 Jun 2026 12:00:00 GMThttps://next.sunisalex.org/en/posts/physics/application-of-the-law-of-gravitation/https://next.sunisalex.org/en/posts/physics/application-of-the-law-of-gravitation/Mon, 08 Jun 2026 12:00:00 GMThttps://next.sunisalex.org/en/posts/physics/universal-law-of-graviation/https://next.sunisalex.org/en/posts/physics/universal-law-of-graviation/Sun, 07 Jun 2026 12:00:00 GMTA panoramic view of the laws of universal gravitation: from Kepler's three laws to the three major cosmic velocities, supplemented by detailed explanations of special topics and examples such as spherical shell gravity, double and triple stars, and celestial energy.https://next.sunisalex.org/en/posts/math/LYW-math-lessons-review/001/https://next.sunisalex.org/en/posts/math/LYW-math-lessons-review/001/Fri, 05 Jun 2026 12:00:00 GMThttps://next.sunisalex.org/en/posts/math/hypergeometric-distribution/https://next.sunisalex.org/en/posts/math/hypergeometric-distribution/Wed, 03 Jun 2026 12:00:00 GMTStarting from the definition, the expectation and variance of the hypergeometric distribution are completely deduced with the help of two combination identities (reduced order formula and Vandermonde identity), and every step is well documented.https://next.sunisalex.org/en/posts/math/beijing-2025-haidian-final-exam-grade11/https://next.sunisalex.org/en/posts/math/beijing-2025-haidian-final-exam-grade11/Wed, 27 May 2026 12:00:00 GMTGiven a positive integer $n(n\ge 3)$, if the sequence $A_n:a_1,a_2,...,a_n$ satisfies the following two properties at the same time, then the sequence $A_n$ is calledhttps://next.sunisalex.org/en/posts/physics/basic-calculus-04/https://next.sunisalex.org/en/posts/physics/basic-calculus-04/Tue, 26 May 2026 12:00:00 GMTUse calculus as a tool to solve physical problems: from the conservation of mechanical energy, simple harmonic motion and elastic potential energy, to the radius of curvature, the principle of virtual work and the variable mass rope, to the kinematics of the micro-element method and the moment of inertia of rigid bodies, and the differential equations and integral ideas in series mechanics.https://next.sunisalex.org/en/posts/physics/basic-calculus-03/https://next.sunisalex.org/en/posts/physics/basic-calculus-03/Sun, 24 May 2026 12:00:00 GMTThis article introduces the application of calculus in physics, covering center-of-mass calculations (cones, hemispheric shells, hemispheres), conservative force potential energy and equilibrium stability criteria, Taylor small quantity expansion and its application in classic problems such as electric dipole forces, relativistic kinetic energy reduction, and non-uniform buoyancy.https://next.sunisalex.org/en/posts/physics/basic-calculus-02/https://next.sunisalex.org/en/posts/physics/basic-calculus-02/Fri, 22 May 2026 12:00:00 GMTStarting from the mass integral, this article systematically introduces the concepts of indefinite and definite integrals, commonly used formulas and substitution methods, and demonstrates the practical application of integrals in competition physics through physical examples such as center of gravity calculation, n-dimensional sphere volume derivation, and resistance motion.https://next.sunisalex.org/en/posts/physics/basic-calculus-01/https://next.sunisalex.org/en/posts/physics/basic-calculus-01/Sun, 17 May 2026 12:00:00 GMTThe calculus covered in this article serves physics competition and focuses on practicality rather than rigorhttps://next.sunisalex.org/en/posts/math/focal-chord-length-formula/https://next.sunisalex.org/en/posts/math/focal-chord-length-formula/Sun, 10 May 2026 12:00:00 GMTThe focal chord length of a conic section is often asked in questions. This article uses straight line parametric equation to derive: - Ellipse - Hyperbola - Parabola The Focus Chohttps://next.sunisalex.org/en/posts/math/AM-GM-inequality-01/https://next.sunisalex.org/en/posts/math/AM-GM-inequality-01/Tue, 05 May 2026 12:00:00 GMTSmall Blueprint "Mean Inequality and Cauchy's Inequality" Chapter 1 After-Class Exercises (Personal Answers)https://next.sunisalex.org/en/posts/android/PJX110-crdroid/https://next.sunisalex.org/en/posts/android/PJX110-crdroid/Sun, 03 May 2026 12:00:00 GMT[!WARNING] The following tutorial is only for OnePlus Ace3Pro to install crDroid 12 (corvette) Irregular gaming, relatives shed tears Readers are responsible for any hardware damaghttps://next.sunisalex.org/en/posts/math/max-minus-min-sequence/https://next.sunisalex.org/en/posts/math/max-minus-min-sequence/Sun, 26 Apr 2026 12:00:00 GMTQuestion (I) enumerates the possible values of $a_4$; question (II) proves that if there is a maximum value, it must contain $0$; question (III) uses proof by contradiction to prove that the positive term sequence has no upper bound: assuming there is an upper bound $M$, we can derive two adjacent items, one large and one small. After three steps of recursion, the large term increases and the small term $2\\times$ is exceeded. Continuous repetition will eventually exceed $M$, contradictory.https://next.sunisalex.org/en/posts/math/hermite-hadamard-inequality/https://next.sunisalex.org/en/posts/math/hermite-hadamard-inequality/Sat, 25 Apr 2026 12:00:00 GMThttps://next.sunisalex.org/en/posts/chemistry/competition/2026-beijing-preliminary/https://next.sunisalex.org/en/posts/chemistry/competition/2026-beijing-preliminary/Sun, 19 Apr 2026 12:00:00 GMTIn the 2026 High School Chemistry Olympiad Beijing Regional Qualifiers, there are no difficult element inferences. It is all about the application of Basic Chemistry Theory and Thehttps://next.sunisalex.org/en/posts/chemistry/competition/2026-summar-vacation-7-12/https://next.sunisalex.org/en/posts/chemistry/competition/2026-summar-vacation-7-12/Sun, 19 Apr 2026 12:00:00 GMTHydrogen Storage Technology (39th Session) 6.1 High-pressure hydrogen storage. Compressed hydrogen is currently one of the most commonly used hydrogen storage methods. Hydrogen ishttps://next.sunisalex.org/en/posts/math/arithmetic-geometric-sequence-lambda/https://next.sunisalex.org/en/posts/math/arithmetic-geometric-sequence-lambda/Sat, 18 Apr 2026 12:00:00 GMTIntroduction It is known that $\{a_n\}$ is an infinite arithmetic sequence with the first term being $a$ and a tolerance of 2. $\{b_n\}$ is an infinithttps://next.sunisalex.org/en/posts/math/sequence-transform-t1-t2/https://next.sunisalex.org/en/posts/math/sequence-transform-t1-t2/Sat, 18 Apr 2026 12:00:00 GMT(2024·Xuzhou Simulation) For the sequence $P:a_1,a_2,\cdots,a_n$ where each item is a positive integer, define transformations $T_1$ and $T_1$ to transform the shttps://next.sunisalex.org/en/posts/math/factor-a3-b3-c3-3abc/https://next.sunisalex.org/en/posts/math/factor-a3-b3-c3-3abc/Sat, 11 Apr 2026 12:00:00 GMTDetailed derivation of the factorization and application of a^3 + b^3 + c^3 - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)