Proof of Concept for a Twin Prime Number Universe Using Set Theory

The Fine Structure Constant (eFSC) Model attempts to give a classical definition to a magical number that underlies much of quantum physics. The Fine Structure Constant (α) value equal to 137.03599206 represents a dimensionless constant that characterizes the strength of the electromagnetic (EM) interaction between subatomic charged particles. Python-generated property counts for the twin prime force F{139/137} show that the adjusted ratio gives a value of α = 137.036. This implies a mathematical framework underlying this constant is based on twin prime numbers and set theory. This study attempts to demonstrate a proof of concept that a hierarchy of fractional twin prime (αII) forces replicates the quantum nature of the universe and is aligned with the Standard Model of Particle Physics. An expanded eFSC Model demonstrates that twin prime forces and their property sets are mathematically viable substitutes for nuclear reactions, as demonstrated for the Beta-minus decay of neutrons into protons. Most significantly, the positive and negative prime numbers define these nuclear reactants and products as positive or negatively charged ions. Furthermore, the eFSC Model provides new insights regarding the hierarchy of EM forces underlying the quantum nature of the universe.

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

Strong Laws of Large Numbers for Fuzzy Set-Valued Random Variables in Gα Space

In this paper, we shall present the strong laws of large numbers for fuzzy set-valued random variables in the sense of d∞H . The results are based on the result of single-valued random variables obtained by Taylor [1] and set-valued random variables obtained by Li Guan [2].

A Strong Law of Large Numbers for Set-Valued Random Variables in Gα Space

In this paper, we shall represent a strong law of large numbers (SLLN) for weighted sums of set- valued random variables in the sense of the Hausdorff metric dH, based on the result of single-valued random variable obtained by Taylor [1].

A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

The Quantum Microverse: A Prime Number Framework for Understanding the Universe

This study aims to demonstrate a proof of concept for a novel theory of the universe based on the Fine Structure Constant (α), derived from n-dimensional prime number property sets, specifically α = 137 and α = 139. The FSC Model introduces a new perspective on the fundamental nature of our universe, showing that α = 137.036 can be calculated from these prime property sets. The Fine Structure Constant, a cornerstone in Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), implies an underlying structure. This study identifies this mathematical framework and demonstrates how the FSC model theory aligns with our current understanding of physics and cosmology. The results unveil a hierarchy of α values for twin prime pairs U{3/2} through U{199/197}. These values, represented by their fraction parts α♊ (e.g., 0.036), define the relative electromagnetic forces driving quantum energy systems. The lower twin prime pairs, such as U{3/2}, exhibit higher EM forces that decrease as the twin pairs increase, turning dark when they drop below the α♊ for light. The results provide classical definitions for Baryonic Matter/Energy, Dark Matter, Dark Energy, and Antimatter but mostly illustrate how the combined α♊ values for three adjacent twin primes, U{7/5/3/2} mirrors the strong nuclear force of gluons holding quarks together.

Binding Number and Fractional k-Factors of Graphs

In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.

基于离散Z+-number集的改进TODIM方法及其应用

针对离散Z+-number环境下的多属性决策问题,将经典的交互式多准则决策方法(TODIM)拓展到Z+-number集中,提出了一种改进的TODIM方法。首先,构造了新的潜藏概率求解模型,实现了离散Z+-number集向离散Z+-number集的转化;然后,通过定义离散Z+-number集的海明距离,计算每个方案相对于其他方案在每个属性下的优势度与总体优势度,并结合优势矩阵计算各方案的综合排序值,从而提出一种基于离散Z+-number集的多属性决策新方法;最后,通过一个风险投资的算例验证了该方法的可行性和稳健性,也为离散Z+-number环境下的决策问题提供了一种新的解决方案。

基于Rough Set的目标快速识别方法

主要研究了基于粗糙集和支持向量机的模式分类技术,结合遥感图像中军用飞机目标识别进行了理论分析和实验研究。设计了基于粗糙集和决策有向无环图的支持向量机模式识别分类器,对分类的性能进行了分析研究,利用粗糙集理论中属性约简方法去除冗余属性,降低飞机特征维数,提出使用决策有向无环图支持向量机进行训练并对待识别目标预测。实验表明,本文提出的方法可提高识别速度及预测分类精度。

优化的Rough Set综合评价算法在房地产开发和销售中的应用

将优化的Rough Set综合评价算法属性的同分辨能力数引入到粗糙集评价,增加了评价的客观性,优化了评价算法,对于房地产开发的决策和综合评价有辅助作用。

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers

A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: MN = 2N – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;MN]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.

Dominating Sets and Domination Polynomials of Square of Paths

Let G = (V, E) be a simple graph. A set S í V is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let be the square of the Path and let denote the family of all dominating sets of with cardinality i. Let . In this paper, we obtain a recursive formula for . Using this recursive formula, we construct the polynomial, , which we call domination polynomial of and obtain some properties of this polynomial.

Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles

Let G = (V, E) be a simple graph. A set S E(G) is an edge-vertex dominating set of G (or simply an ev-dominating set), if for all vertices v V(G);there exists an edge eS such that e dominates v. Let denote the family of all ev-dominating sets of with cardinality i. Let . In this paper, we obtain a recursive formula for . Using this recursive formula, we construct the polynomial, , which we call edge-vertex domination polynomial of (or simply an ev-domination polynomial of ) and obtain some properties of this polynomial.

A POLYNOMIAL ALGORITHM FOR FINDING THEMINIMUM FEEDBACK VERTEX SET OF A3-REGULAR SIMPLE GRAPH

A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.

The Total Irredundance Numbers on Graphs

This paper discusses the total irredundance relations between the graph G and its clone-contraction graph H, that is, let H be the clone-contraction graph of G and v1,v2,...,vk be all contraction vertices ofH. IfS is a maximal total irredundant set of H such that A = S ∩ {V1,V2,…,Vk} contains as few vertices as possible, then S＇= S-A is the maximal total irredundant set of G. Furthermore, we obtain the bound of the total irredundance A（G） number： irt ≤△（G）/2△（G）＋1 n, which n is the order of graph G, and △（G） is maximum degree in G.

On Locating Numbers of Graphs

Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W is said to be a locating set of G if distinct vertices have the distinct locating code,and the locating number of G is defined as: Loc( G) = min{ | W| : W is a locating set of G}.We study the locating set and locating number of a graph G,obtain some bounds for the locating numbers of graphs,and determine the exact value of Loc( G) for some special classes of graphs,such as cycles,wheels,complete t-partite graph and some Cartesian products of paths and cycles. In addition,we also prove that Loc( T) ≥Δ-1 holds for all trees T with maximum degree Δ,and shows a tree T with Loc( T) = Δ-1.

Quasi-cardinality of a Fuzzy Set on a Measurable Universe of Discourse

The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some properties of them are given out and thus some relevant results are elucidated.

基于集对分析的区域水利高质量发展评价方法

基于发展目标、发展途径、发展条件相作用形成的区域水利高质量发展系统结构和相对联系数的指标体系筛选方法,构建了由59个评价指标、11个发展方面、3个发展子系统组成的区域水利高质量发展评价指标体系;利用专家咨询和遗传层次分析法确定各指标权重,采用集对分析计算指标、方面、子系统和样本4个层次与区域水利高质量发展评价标准集对间的联系数,应用减法集对势判断4个层次区域水利高质量发展状态,建立了基于集对分析的区域水利高质量发展评价方法(SPA-HDEM),并将其应用于陕西省2020年10个地市的水利高质量发展评价中。结果表明:西安水利高质量发展状态处于中等偏较高等级,咸阳、汉中、渭南、安康、宝鸡、榆林均处于中等等级,延安、商洛、铜川均处于较低偏中等等级;非陕南的7个地市的发展条件均不佳,10个地市的发展途径均相对较低;各地市处于反势的指标中,西安有“人均水资源量”等11个、铜川有“防洪堤防达标率”等32个、宝鸡有“水利投资占GDP比重”等16个、咸阳有“人均生活用水量”等14个、渭南有“水资源开发利用率”等19个、延安有“供水模数”等21个、榆林有“供水模数”等22个、汉中有“防洪堤防达标率”等15个、安康有“防洪堤防达标率”等21个、商洛有“人均工资”等25个,重点调控这些反势指标是全省水利高质量发展工作中的重要任务。SPA-HDEM适用性强,在已知评价等级标准的实际区域水利高质量发展评价问题中具有应用前景。