New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Reverse Dimension Dominating As Hyper Dimple On Super Dimity
Henry Garrett · Zenodo (CERN European Organization for Nuclear Research) · 2023
285 Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Reverse Dimension Dominating As Hyper Dimple On Super Dimity”, Zenodo 2023, (doi: 10.5281/zenodo.8072171). @ResearchGate: https://www.researchgate.net/publication/- @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/8072171 @academia: https://www.academia.edu/- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar ewtheorem{theorem}{Theorem}[section] ewtheorem{lemma}[theorem]{Lemma} ewtheorem{proposition}[theorem]{Proposition} ewtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} ewtheorem{definition}[theorem]{Definition} ewtheorem{example}[theorem]{Example} ewtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} ewtheorem{remark}[theorem]{Remark} \theoremstyle{observation} ewtheorem{observation}[theorem]{Observation} \theoremstyle{question} ewtheorem{question}[theorem]{Question} \theoremstyle{problem} ewtheorem{problem}[theorem]{Problem} umberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf ewline{ New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Reverse Dimension Dominating As Hyper Dimple On Super Dimity } } ewline ewline Henry Garrett · Independent Researcher · Department of Mathematics · [email protected] · Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyper{\tiny Reverse Dimension Dominating}). Let a Neutrosophic SuperHyperGraph (NSHG) $S$ be a {\tiny Reverse Dimension Dominating} pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V'=\{V_1,V_2,\ldots,V_s\}$ and $E'=\{E_1,E_2,\ldots,E_z\}.$ Then either $V'$ or $E'$ is called Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating} if the following expression is called Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating} criteria holds \begin{eqnarray*} && \forall E_a \in E_{NSHG}, \exists E_b\in E': \exists V_c\in V_{NSHG}, V_c\in E_a,E_b \\&& \text{And} ~\forall E_a,E_b \in E_{NSHG}, \exists E_c\in E': d(E_a,E_c)\leq d(E_b,E_c); \end{eqnarray*} Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating} if the following expression is called Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating} criteria holds \begin{eqnarray*} && \forall E_a \in E_{NSHG}, \exists E_b\in E': \exists V_c\in V_{NSHG}, V_c\in E_a,E_b \\&& \text{And} ~\forall E_a,E_b \in E_{NSHG}, \exists E_c\in E': d(E_a,E_c)\leq d(E_b,E_c); \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPHIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPHIC CARDINALITY}};$ Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating} if the following expression is called Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating} criteria holds \begin{eqnarray*} && \forall V_a, \exists V_b\in V': \exists E_d\in E_{NSHG}, V_a,V_c\in E_d \\&& \text{And} ~\forall V_a,V_b \in V_{NSHG}, \exists V_c\in V': d(V_a,V_c)\leq d(V_b,V_c); \end{eqnarray*} Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating} if the following expression is called Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating} criteria holds \begin{eqnarray*} && \forall V_a, \exists V_b\in V': \exists E_d\in E_{NSHG}, V_a,V_c\in E_d \\&& \text{And} ~\forall V_a,V_b \in V_{NSHG}, \exists V_c\in V': d(V_a,V_c)\leq d(V_b,V_c); \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPHIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPHIC CARDINALITY}};$ Neutrosophic SuperHyper{\tiny Reverse Dimension Dominating} if it's either of Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating}, and Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating}. ((Neutrosophic) SuperHyper{\tiny Reverse Dimension Dominating}). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyper{\tiny Reverse Dimension Dominating} if it's either of Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating}, and Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Reverse Dimension Dominating}; a Neutrosophic SuperHyper{\tiny Reverse Dimension Dominating} if it's either of Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating}, and Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating} and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Reverse Dimension Dominating}; an Extreme SuperHyper{\tiny Reverse Dimension Dominating} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating}, and Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating} and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Reverse Dimension Dominating}; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyper{\tiny Reverse Dimension Dominating} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic re-SuperHyper{\tiny Reverse Dimension Dominating}, Neutrosophic v-SuperHyper{\tiny Reverse Dimension Dominating}, and Neutrosophic rv-SuperHyper{\tiny Reverse Dimension Dominating} and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic Super