21 found
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  1.  90
    Analyzing the Zeros of the Riemann Zeta Function Using Set-Theoretic and Sweeping Net Methods.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:15.
    The Riemann zeta function ζ(s) is a central object in number theory and complex analysis, defined for complex variables and intimately connected to the distribution of prime numbers through its zeros. The famous Riemann Hypothesis conjectures that all non-trivial zeros of the zeta function lie on the critical line Re(s) = 1 2 . In this paper, we explore the Riemann zeta function through the lens of set-theoretic and sweeping net methods, leveraging creative comparisons of specific sets to gain deeper (...)
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  2.  62
    Non-Commutative Scalar Fields.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:9.
    In this paper, we explore numerical methods for simulating scalar field con-figurations in non-commutative two-dimensional spaces. We focus on the finite difference techniques employed to compute mixed partial derivatives and the action functional in the presence of non-commutative corrections. The methods presented address the challenges posed by non-commutative geometry, specifically in computing the mixed derivative terms that arise due to the deformation of spatial coordinates. We introduce semi-implicit time-stepping schemes to en-sure numerical stability when dealing with stiff nonlinear terms. The (...)
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  3.  62
    Cohesive Logic Vectors.Parker Emmerson - manuscript
    We have now mapped the set of analogies Ai,j to conceptual and mechanical meanings. This allows us to recognize how the Group Algebraic System G decomposes into five smaller subsystems, each of which relate to well-known symbolic systems. Furthermore, by recognizing the algorithmic transformations between these subsystems, we can apply each representing a single component of the Group Algebraic System G, or model how algorithms are used in mathematics, by mapping its meaning onto the corresponding transformation steps between the subsystems. (...)
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  4.  60
    Optimized Energy Numbers Continued.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:12.
    In this paper, we explore the properties and optimization techniques related to polyhedral cones and energy numbers with a focus on the cone of positive semidefinite matrices and efficient computation strategies for kernels. In Part (a), we examine the polyhedral nature of the cone of positive semidefinite matrices, , establishing that it does not form a polyhedral cone for due to its infinite dimensional characteristics. In Part (b), we present an algorithm for efficiently computing the kernel function on-the-fly, leveraging a (...)
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  5.  53
    Defining π via Infinite Densification of the Sweeping Net and Reverse Integration.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1 (1):7.
    We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition from (...)
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  6.  52
    The Nuances of Deprogramming Zeros.Parker Emmerson - 2024 - Journal of Liberated Mathematics.
    Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties of (...)
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  7.  54
    The Book of Phenomenological Velocity: Algebraic Techniques for Gestalt Cosmology, Transcendental Relativity and Quantum Mechanics.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:380.
    If you have enjoyed any of the 7 (seven) other books I have published over 20 years, including literally thousands of pages of mathematical and topological concepts, Python programs and conceptually expanding papers, please consider buying this book for $20.00 on google play books. -/- Introduction: -/- Though the following pages provide extensive exposition and dedicated descriptions of the phenomenological velocity formulas, theory and mystery, I thought it appropriate to write this introduction as a partial explanation for what phenomenal velocity (...)
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  8.  50
    Formalizing Mechanical Analysis Using Sweeping Net Methods.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:12.
    We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.
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  9.  46
    Cone Formation from Circle Folding: A Comprehensive Analysis.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:4.
    This paper explores the mathematical details behind the geometric transformation of folding a circle into a cone. It includes detailed theo- rems, proofs, and Python implementations for visualization, providing a thorough analysis of the transformation process.
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  10.  46
    Motivic Operators and M-Posit Transforms on Spinors.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:34.
    Spinor theory and its applications are indispensable in many areas of theoretical physics, especially in quantum mechanics, general relativity, and string theory. Spinors are complex objects that transform under specific representations of the Lorentz or rotation groups, capturing the intrinsic spin properties of particles. Recent developments in mathematical abstraction have provided new insights and tools for exploring spinor dynamics, particularly through the lens of motivic operators and M-Posit transforms. This paper delves into the intricate dynamics of spinors subjected to motivic (...)
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  11.  42
    Journal article Open Formalizing Mechanical Analysis Using Sweeping Net Methods II: Written Without Complex Analysis and With Complex Analysis.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1:13.
    Published with great thanksgiving for Yaohushua, the living One Yahowah, "Jesus Christ." -/- In previous work, Formalizing Mechanical Analysis Using Sweeping Net Methods I, sweeping net methods have been extended to complex analysis, relying on the argument of complex functions defined on the unit circle. In this paper, we reformulate these methods purely within a real-valued and geometric framework, avoiding the use of complex analysis. By redefining the sweeping net constructs and the associated theorems using real functions and geometric interpretations (...)
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  12.  40
    Optimized Energy Numbers.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1 (1):36.
    We recall, "a priori," numeric energy expression: -/- Energy Numbers -/- $\begin{gathered}\mathcal{V}=\left\{f \mid \exists\left\{e_1, e_2, \ldots, e_n\right\} \in E \cup R\right\} \\ \mathcal{V}=\left\{f \mid \exists\left\{e_1, e_2, \ldots, e_n\right\} \in E, \text { and }: E \mapsto r \in R\right\} \\ \mathcal{V}=\left\{E \mid \exists\left\{a_1, \ldots, a_n\right\} \in E, E \not \neg r \in R\right\}\end{gathered}$ -/- We now introduce the set of optimized energy numbers: -/- ($H_a \in \mathcal{H}$ or $P^n = NP$ or $(P,\mathcal{L},F) = NP$). -/- Based on our formulation of (...)
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  13.  38
    S - The Set Where Counting is Impossible.Parker Emmerson - 2024 - Journal of Liberated Mathematics 1 (1):3.
    In this paper, we define and explore the mathematical space S, a system where traditional numerical elements like natural numbers are undefined due to the non-evaluability of certain integrals. We investigate how purely formal and logical structures can be constructed within S without numerical interpretations, and we explore how the concept of infinity can be approached within this framework. The document also includes discussions on the implications, applications, and potential future explorations within S.
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  14.  71
    Phenomenological Velocity.Parker Emmerson - 2023 - Journal of Liberated Mathematics 1:10.
    Abstract: The intent of this paper is to provide a simple focus on that math- ematical concept and solution, phenomenological velocity to shine light on a worthy topic for mathematicians and physicists alike. Phenomenological Veloc- ity is essential to the formulation of a gestalt cosmology. The bibliography of this paper provides references to the extensive research that has been conducted by myself on the topic. I have performed conditional integrals of the phenomeno- logical velocity in its most liberated standard-algebraic form, (...)
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  15.  57
    The Sphere of Realization: The Mathematical Path of Harmonious Balance.Parker Emmerson - 2023 - Zenodo.
    From The Cone of Perception, volume one of my collected works, you will remember that one of the main topics in that work was V-Curvature, also called, "phenomenological velocity." In that work, although a solution to the v - curvature variable was provided as well as many graphs that yielded numerous jewels of spiral formulations in exquisite 3D color formations, that method by which the solution was found was not iterated. This chapter begins by showing how it is possible to (...)
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  16.  50
    Exploring the Possibilities of Sweeping Nets in Notating Calculus- A New Perspective on Singularities.Parker Emmerson - unknown
    The paper proposes a method for approximating surfacing singularities of saddle maps using a sweeping net. The method involves constructing a densified sweeping subnet for each individual vertex of the saddle map, and then combining each subnet to create a complete approximation of the singularities. The authors also define two functions $f_1$ and $f_2$, which are used to calculate the charge density for each subnet. The resulting densified sweeping subnet closely approximates the surfacing saddle map near a circular region.
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  17.  49
    Conditional Integral of Phenomenological Velocity V. 5.0 (5th edition).Parker Emmerson - 2022 - Journal of Liberated Mathematics 1:47.
    Higher - dimensional calculus and integral transformation play crucial roles in advancing our understanding of complex systems in mathematics and theoretical physics . Integral transformations are instrumental in simplifying complex differential equations, enabling the resolution of multi - dimensional problems that arise in various scientific fields . This paper aims to delve into a specific higher - dimensional integral transformation defined by the axioms \(F[q, s, l, \alpha]\) and \(G[q, s, l, \beta, c]\) . We start by outlining the axioms (...)
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  18.  46
    Chaos and Authaumatronics.Parker Emmerson - 2024
    Chaos topology delves into bizarre symbol configurations of the world of quasi-quantification and pseudo-quantifiability. With quantum complexes, we are eventually able to find game play that blends wormholes with quantum computers and transcendental numbers. A conclusion that will leave you breathless, Chaos (Emmerson, 2023),.
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  19.  40
    Limbertwig.Parker Emmerson - 2023
    This work is a attempt to describe various braches of mathematics and the analogies betwee them. Namely: 1) Symbolic Analogic 2) Lateral Algebraic Expressions 3) Calculus of Infin- ity Tensors Energy Number Synthesis 4) Perturbations in Waves of Calculus Structures (Group Theory of Calculus) 5) Algorithmic Formation of Symbols (Encoding Algorithms) The analogies between each of the branches (and most certainly other branches) of mathematics form, ”logic vectors.” Forming vector statements of logical analogies and semantic connections between the di↵erentiated branches (...)
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  20.  32
    The Cone of Perception.Parker Emmerson - 2010
    I write this introduction with much work already completed in this 4th Edition of The Cone of Perception, primarily to frame the work and touch on what might be missing from it. Namely → though it is hardly lacking these, I’d like to add a few insights about the content of the work and its relevance to the subject and future technology. Why is this work still relevant? How can you use it in your work/subject/area/field, and how am I supposed (...)
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  21.  42
    The Math of Liberation: A New Language for Balancing Within (Second Edition) (Book 3 in Series).Parker Emmerson - 2022
    For praising Jehovah (Yahowah is Yeshua Ben Joseph) do I publish these mathematical gesturing forms by His graciousness. The Book of Eternity proposes a new, mathematical balancing language in which the logic stems from infinity instead of zero. The designation of the balance comes from the location at which different meanings of infinity linguistically balance with each other and provides a way for people to continue extrapolating forms and functions that logically would follow. This balancing at oneness is analogous to (...)
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