Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Mapping of the Main Functions and Different Variations of YH-DIE

Version 1 : Received: 25 August 2020 / Approved: 26 August 2020 / Online: 26 August 2020 (10:19:32 CEST)

How to cite: Mason, G.; Chou, Y.; Pind, S. The Mapping of the Main Functions and Different Variations of YH-DIE. Preprints 2020, 2020080578 (doi: 10.20944/preprints202008.0578.v1). Mason, G.; Chou, Y.; Pind, S. The Mapping of the Main Functions and Different Variations of YH-DIE. Preprints 2020, 2020080578 (doi: 10.20944/preprints202008.0578.v1).

Abstract

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

Subject Areas

complete Riemannian manifolds; entire solutions; minimal graphs; differential equat; algebraic variety

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