It was rush hour on Subway Line 10. Wei Ling gripped the overhead handrail, his body swaying back...
Wei Ling set a small bunch of white chrysanthemums against the rail of Hongqiao Bridge. The river...
The First Love --- Some social news left Wei Ling with a tangled mess of feelings. He couldn't...
The wheels spun wildly! From Haicheng to Lincheng, westbound, day and night. Wind...
Somehow, Wei Ling had been staying home a lot lately. That night, he lay on the couch and...
Wei Ling sat cross-legged on the sofa, a bowl of instant noodles balanced on his knee. The cold...
Feminism had flourished for two hundred years. Women had fought for and won countless rights,...
The day Liu Ezi went to the school to see Teacher Zhang, she had discussed it with Yan...
Yan Gaoshan got hired by the factory in town. It was an agricultural machinery repair...
--- It was the kind of afternoon that made you feel sorry for yourself. The sun was brutal—hot...
Numerical Cases and Analysis of Two Basic Navier-Stokes Formulas Author: Zhang Suhang Version 1: Basic Paradigm (ECS + DOG + MlE) boldsymbol{U}^{n+1} =mathop{argmin}{boldsymbol{U}inmathcal{H}} mathcal{E}big(boldsymbol{U},nablaboldsymbol{U}big) ...
Hierarchical Classification, Applicability Boundaries, and Value Analysis of Three Types of Flow Control Formulas under the Navier-Stokes System Author: Zhang Suhang AbstractRegarding the four core equations derived from the Multi-Origin Coordin...
A Topological Extremum Solving Method for the Navier-Stokes Equations Based on the boldsymbol{Pi} Projection Operator and the MOC-DOG-ECS-MlE Framework
Author: Zhang Suhang
1. Introduction The Navier-Stokes (NS) equations serve as the cor...
Paper III: Global Unification of the Three Underlying Physical Systems of Mechanics, Geometry, and Energy via ECS Author: Zhang Suhang (Heluo School of Mathematics) AbstractBy integrating the complete set of derivations with newly established me...
Paper II: Rigorous Derivation of Symplectic Structure Breakdown (Proof of the Degeneration of the Symplectic Form boldsymbol{omega}) Author: Zhang Suhang (Heluo School of Mathematics) Prerequisite KnowledgeFor a finite-dimensional Hamiltonian sy...
Paper I：Rigorous Chain Mapping of Action–Potential Difference–Stability: The Local Reduction Essence of Symplectic Structure and Global Unification under ECS Author: Zhang Suhang (Heluo School of Mathematics) AbstractIn the classical mechanics s...
God makes all things with the greatest economy and efficiency. That is the essence of MlE. MlE provides mathematical support for Darwin's theory of evolution. Redundant structures that serve no purpose and consume resources t...
From Newton to Riemann, from fluxions to manifolds. Everything flows, nothing stands still. Is mathematics really so dull and boring? I don't think so!
Proof That the Sphere Has the Minimal Surface Area Among Rotational Solids of Equal Volume (Rotational Case of the 3D Isoperimetric Inequality) Author: Zhang Suhang Conventional Approach The conventional proof relies on calculus of va...
Supplemental Paper S‑05: Unification of Factorial System via Three-Channel Π Operators: Operator Formalization of Combinatorics, Factorials and the Gamma Function Author: Suhang Zhang Abstract Factorials, combinatorial counting and th...
Supplemental Paper S‑04: Probabilistic Π Operators and Dimensional Transformation Theory for Stochastic ProcessesAuthor: Suhang Zhang, Heluo School of MathematicsAbstractThe classical Π operator framework has been established with a dual contin...
Supplemental Paper S‑03: Global Generalization of the Π Operator within the Framework of DOG Discrete Order Geometry Author: Suhang Zhang, Heluo School of Mathematics Abstract The conventional Π operator system is constructed upon t...
Supplemental Paper S‑02: Definition of Generalized Π Operators under the MOC (Multi‑Origin Curvature Geometry) Framework Author: Suhang Zhang (Heluo School of Mathematics) Abstract The canonical three-channel Π operator system estab...
Supplemental Paper S‑01: From Linear Approximation to Higher‑Dimensional Tiling: Channel Unification and Dimensional Transition within Euler’s and Ramanujan’s Series under the Π Operator Framework Author: Suhang Zhang (Heluo School of Mathemat...
Paper 5-3: Prospect of System Expansion: Interdisciplinary Developments toward Non-Euclidean Manifolds, Quantum Field Theory and Advanced Number Theory Author: Suhang Zhang (Heluo School of Mathematics) Abstract The Π operator frame...
Paper 5-2: Historical Review on the Evolution of π Research: From Euler and Ramanujan to the Formulation of the Π Operator System Author: Suhang Zhang (Heluo School of Mathematics) Abstract The cognitive history of π consists of three ...
Paper 5-1: Applications of the Π Operator in Engineering: 3D Modelling, Rotary Mechanisms and Periodic Oscillations Author: Suhang Zhang (Heluo School of Mathematics) Abstract The Π operator framework establishes a unified mathematical...
Paper E4-4: Generator Relations between Euler’s Formula and the Π-Operator Author: Suhang Zhang (Heluo School of Mathematics) Abstract Euler’s formula e^{i\theta}=\cos\theta+i\sin\theta intrinsically links complex exponentials to circu...
Paper 4-3: A Study on the Complementarity between the Π-Operator and Classical Differential OperatorsAuthor: Suhang Zhang (Heluo School of Mathematics)AbstractClassical differential operators including gradient, divergence, curl, Laplacian, d'Ale...
Paper 4-2: Integral Channel: Cross-Dimensional Π Mapping of Scalar and Vector FieldsAuthor: Suhang Zhang, Heluo Mathematical SchoolReferences: OmittedAbstractThe Channel III of the Π operator relies on integral-type π quantities (Gaussian integral...