A Topological Extremum‑Seeking Solver for the NS Equations Based on the MOC‑DOG‑ECS‑MlE Framework 1 Introduction The Navier‑Stokes (NS) equations constitute the core governing system of viscous fluid dynamics. Conventional CFD solvers are ...
A Preliminary Study on the Unified Description of Energy, Classical Mechanics and Symplectic Geometry Based on the ECS FrameworkAuthor: Zhang Suhang (Luoyang School of Mathematics)AbstractBased on the proposed ECS framework, this paper explores ...
Paper II: Rigorous Derivation of Symplectic Structure Breakdown (Proof of the Degeneration of the Symplectic Form boldsymbol{omega}) Author: Zhang Suhang (Luoyang School of Mathematics） Prerequisite KnowledgeFor a finite-dimensional Hamiltonian ...
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!
Paper 2-1: Dual-Channel Transformation of the Π Operator for Cylindrical Bodies
Author: Zhang Suhang （Luoyang School of Mathematics） Abstract
A cylinder is the simplest non-spherical solid of revolution. Its formation intrinsically corre...
URFE Calculates the Hohmann Window
Author: Zhang Suhang
Abstract
The following directly uses URFE → Newtonian gravity + Keplerian orbits to calculate, without extraneous detail, the launch time and orbital parameters for minimum fuel c...
URFE Calculates the Four Fundamental Forces
Based on the Unified Recursive Field Equation (URFE), this paper selects typical calculable scenarios, applies boundary conditions, performs quantitative simplif...
URFE Calculates Celestial Orbits
Combining the Unified Recursive Field Equation (URFE) with scenario-based calculations for different gravitational field strengths, and following the previously defined symb...
URFE （ Zhang Suhang Equation） Solves the Three-Body Problem Author: Zhang Suhang 1. First: What Makes the Classical "Three-Body Problem" Difficult Standard Conclusion (holds from 1880 to 2026): · No general elementary analytic solution: The po...
Derivation of the Four Fundamental Interactions from the Unified Recursive Field Equation (URFE，Zhang Suhang Equation） Author: Zhang Suhang
Abstract: Based on the Unified Recursive Field Equation (URFE), parameter partitioning, group subspac...
Complete Derivation of the Unified Recursive Field Equation (URFE) Author: Zhang Suhang
1. Core Prerequisite Theories
Foundation: MOC Multi-Origin Geometry, DOG Discrete Order Geometry, GPCL Geometric Recursive Conservation Chain, Unifie...
--- 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 ...
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Dynamic Vector Geometry（DVG）: A Research Programme
Author: Zhang Suhang Luoyang School of Mathematics September 2026
This paper proposes a research programme aimed at generalizing the fundamental objects of geometry from...
Foundations of Arithmetic Manifold Geometry — A Programmatic OutlineAuthor: Zhang SuhangDate: May 2026AbstractIn traditional mathematics, geometry, mapping theory and number theory have long developed separately: differential geometry investigates...
--- MOC Coordinate System: Geometric Definition of Multi-Origin Hierarchical Nesting and Degeneration to Classical Coordinates Author: Suhang Zhang --- Abstract Based on the Multi-Origin Curvature (MOC) geometric framework, this paper prese...
--- The Dimensional Mapping Generative Principle of Number Bases: A Unified Geometric Origin of Discrete, Linear, and Periodic Numeral Systems
This paper addresses the fundamental problem of the origi...
A Universal Resolution Theory for Self-Reference Paradoxes Based on MOC Multi-Origin Curvature Geometry
Author: Zhang Suhang (Founder of the Heluo Mathematical School)
Self-reference paradoxes have stood as a core conundrum pla...
--- Resolution of the Barber Paradox within the MOC (Multi-Origin Curvature) Geometric Framework
The Barber paradox (a popular version of Russell's paradox) reveals the logical contradiction arising from "se...
--- High-Dimensional Truth Gap: The Geometric Root of Gödel Incompleteness and Quantum Uncertainty
Author: Zhang Suhang, Luoyang, Henan
Gödel's incompleteness theorems reveal the existence of undecidable propositions in f...
Chapter 7： Conclusions and Outlook: Classical Logic as a Special Case of MOC Logic — Toward a New Hierarchical Logic System Author: Zhang Suhang, Luoyang, Henan Abstract This is the final chapter of the series Geometric Origin of th...
Chapter 6 ：Reconstruction of the Three Fundamental Laws of Logic: The Law of Identity, the Law of Contradiction and the Law of Excluded Middle as Products of Low-Dimensional Projection Author: Zhang Suhang, Luoyang, Henan Abstract This...
Chapter 5 The Emergence of Binary: Symbolization of the Law of Excluded Middle — Binary is the minimal symbol set of the law of excluded middle, and numeral systems are counting modes after projection Author: Zhang Suhang (Luoyang, Hena...
Chapter 4: Projection Mapping \boldsymbol{\Pi} and State Collapse Mechanism: \boldsymbol{\Pi: \mathcal{T}\to\{0,1\}}, Forced Binarization and Emergence of the Law of Excluded Middle Author: Zhang Suhang, Luoyang, Henan Abstract ...
Chapter 3: Three Non-Classical States of the High-Dimensional Truth Space \mathcal{T} Further elaboration: Definitions of truth-value gap, truth-value glut and indeterminate state Author: Zhang Suhang (Luoyang, Henan)
This pa...
Chapter 2: The Higher-Dimensional "OR" State: The Matrix of the Law of Excluded Middle Author: Zhang Suhang (Luoyang, Henan, China) Abstract This paper is the second installment in the research series Geometric Origin of the Law of Exc...
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...
Tree Root-Shoot Isomorphism: A Natural Empirical Validation of Information Topology Author: Zhang Suhang --- Abstract This paper does not aim to investigate the growth patterns of plant organs. Rather, it selects the reversible transformation ...
--- 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...