The day Liu Ezi went to the school to see Teacher Zhang, she had discussed it with Yan...
URFE Calculates Celestial Orbits
Author: Zhang Suhang
Abstract
Combining the Unified Recursive Field Equation (URFE) with scenario-based calculations for different gravitational field strengths, and following the previously defined symb...
--- MOC Coordinate System: Geometric Definition of Multi-Origin Hierarchical Nesting and Classical Coordinate Degeneration
Author: Zhang Suhang Founder of the Heluo Mathematical School
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Based on the Multi-Origin Curvature...
Chapter 1：Geometric Origin of the Law of Excluded Middle The Emergent Essence of Classical Logical Laws under the MOC Framework
Author: Zhang Suhang (Luoyang, Henan, China)
Chapter 1 Introduction: The Sanctity and Fractures of the L...
--- Native Derivation of Yang-Mills Equations within the DOG Framework (Under the Unified Four-Force Paradigm) Author: Zhang SuhangAffiliation: Independent Researcher, Luoyang, Henan --- Abstract Traditional Yang-Mills theory is a field-theor...
Discrete Order Geometry (DOG) First‑Principles Derivation of the Dirac Equation: Spinor Order and Relativistic Discrete Evolution
Author: Zhang Suhang (Luoyang, Independent Researcher)
Abstract – Based on the unified discrete evolution p...
Title: Research on Extremum-Conservation-Symmetry (ECS) Discrete System Modeling and Laws of Large Numbers Author: Zhang Suhang (Luoyang) Abstract: This paper conducts systematic theoretical research on Extremum-Conservation-Symmetry (ECS) discr...
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 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...
--- Integrating All Physical Elements and Factors into the Geometric Recursive Conservation Chain（UGSL）: A Unified Logical Framework
I. General Outline: The Universal Conservation Rule for All Physical Elements
Core ...
Markov Theory as a Strict Special Case of the UPGS Universal Axiom System
Author: Zhang Suhang (Founder of the He-Luo Mathematical School)
This paper independently, purely, and rigorously demonstrates the axiomatic hierarchy a...
The Dual Constant Dynamic-Static Unification Principle in the DOG System
Author: Zhang Suhang Address: Luoyang, Henan
Within the complete framework of DOG discrete order geometry, the universe's two most fundamenta...
Under the MOC paradigm, the complete analytical equations for the gravitational three-body problem of the Earth, Moon, and Sun. Author: Zhang Suhang (followed by the detailed sections I–IV as in your Chinese text) …Is this acceptable? My res...
The Impact of Multi-Origin High-Dimensional Geometry on Radar DesignIn modern national defense and detection systems, radar has long been more than a device for detecting targets. It serves as a core strategic equipment supporting battlefield situ...
Paper 3-2: Composite Transformations and the Structure of Dimensional Transformation Group Author: Suhang Zhang (Heluo Mathematical School) Abstract The core function of the \Pi-operator is to perform mapping operations between spac...
Paper 2-1: Dual-Channel Transformation of the Π Operator for Cylindrical Bodies Author: Zhang Suhang (Heluo Mathematical School) Abstract A cylinder is the simplest non-spherical solid of revolution. Its formation intrinsically corr...
Paper 5: Stochastic Processes and Geometric Flows: From Random Walks to Brownian Motion and Quantum Probability Author: Zhang Suhang Affiliation: Luoyang, Henan Abstract This paper extends the probability-geometry isomorphism frame...
Discrete Order Geometry (DOG) and Harmonic Analysis: A Unified Framework for Decomposition and Reconstruction of Smooth Fields
Author: Zhang Suhang Independent Researcher · Luoyang
This paper establishes a fundamental com...
DOG Primitive Theorem: Natural Emergence of Algebraic Cycles in Discrete Order Geometry
Algebraic cycles (algebraic subvarieties) are the central objects of the Hodge conjectur...
ECS Symmetry Conservation and the Principle of Least Action Author: Zhang Suhang(Independent Researcher, Luoyang) System Affiliation: MOC–MIE–ECS–UCE Unified Mathematical-Physical ParadigmSeries Number: Seventh Paper --- Abstract As the openi...
A Topological Extremum Solving Method for the Navier-Stokes Equations Based on the boldsymbol{Pi} Projection Operator and the MOC-DOG-ECS-MlE Framework
1. Introduction The Navier-Stokes (NS) equations serve as the cor...
Paper 1-3: Architecture of Three Major Transformation Channels Based on Multiple Expressions of π
Author: Zhang Suhang (Heluo Mathematical School)
The core innovation of the \mathcal{\Pi} operator lies in the fact that differe...
--- Part IV: Discrete Origin and Continuous Limit: The Unified Resolution of Binary Forms in the New Set Theory Author: Zhang Suhang, Luoyang, Henan Abstract The binary fragmentation between discrete and continuous is one of the longest-standi...
DOG Discrete Order Geometry and Lattice Theory: Algebraic Representation of Order Structures Author: Zhang SuhangAddress: Luoyang, Henan --- Abstract Lattice theory studies algebraic structures in which any two elements in a partially ordered ...
Somehow, Wei Ling had been staying home a lot lately. That night, he lay on the couch and...
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 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...
--- Part III: Subordination Relations, Nesting Rules, and Cross-Layer Mapping Systems for Hierarchical Sets Author: Zhang Suhang, Luoyang, Henan Abstract Building upon the establishment of the hierarchically nested set paradigm and the three-l...
Renormalization Group Equations for Quantum Gravity Based on the Discrete Parent GroupAuthor: Suhang Zhang, Luoyang, HenanAbstractThe ultraviolet divergences in quantum gravity originate from the assumption of infinitely differentiable continuo...
Proof of the Twin Prime Conjecture within the DOG/MOC/ECS/MIE Framework
The twin prime conjecture is a century‑old core problem in analytic number theory. Its weak version, p...