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To the Function of the Objet a – Natalia Rebrova
In this text, the objet a is approached beyond its classical psychoanalytic formulation, not merely as the object-cause of desire, but as a topological effect of displacement, marked in the structure as an irreducible differential. The objet a does not exist as an entity, it is not localized in space or time; it manifests only
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A Linear Algebraic Structure in the Collatz Map Proving Convergence – Adhil Sony
We explore the behavior of a subset of the Collatz map through linear transformations, deriving conditions under which the iteration admits a rational and positive eigenvalue. This structure suggests potential constraints on divergence and dependencies within the map. Peer-review this article by using the comments or upvoting/downvoting
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On the Unique Steady State of a Reduced Collatz Dynamical System – Adhil Sony
We explore the behavior of a subset of the Collatz map through linear transformations, deriving conditions under which the iteration admits a rational and positive eigenvalue. This structure suggests potential constraints on divergence and dependencies within the map and finds the existence and uniqueness of the loop in the iterative map. Peer-review this article by
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Analysis of the Collatz Map: Digital Root Behavior and Loop Impossibility – Adhil Sony
In this paper, we present a novel analysis of the Collatz conjecture. We explore the digital root behavior of numbers under the Collatz map and identify a consistent mapping pattern based on modular arithmetic properties. Furthermore, we introduce a rigorous argument showing that the only possible closed loop in the Collatz map is the trivial
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Generalized Loop Equivalence Conjecture – Adhil Sony
This paper proposes the Generalized Loop Equivalence Conjecture, which states that the recurrence relation an + k has the same number of loops as an + kap for any integer p ≥ 1. The conjecture explores the equivalence of loops formed by different mappings, identifying patterns based on the multiplier and additive constants. The paper
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The global existence of small-amplitude solutions to nonlinear Klein-Gordon equations: A study based on S. Klainerman’s approach – Alessandro Massaad
In this thesis we explore S. Klainerman’s proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985 [KLM1985]. We consider initial data with small amplitude and compact support and aim prove the global existence and uniform decay of smooth solutions. We
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Refining and Robust Backtesting of A Century of Profitable Industry Trends – Alessandro Massaad et.al.
We revisit the long-only trend-following strategy presented in A Century of Profitable Indus- try Trends by Zarattini and Antonacci [1], which achieved exceptional historical performance with an 18.2% annualized return and a Sharpe Ratio of 1.39. While the results outperformed benchmarks, practical implementation raises concerns about robustness and evolving market conditions. This study explores modifications
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On the Non-existence of Exponential Calculus – Thilakraj Bhandary and Aryan Chand
In 2008 Bashirov-Kurpınar-O ̈zyapıcıin [1] generalized the notion of multiplicative calculus introduced by Grossman-Katz [2]. In this paper we explore whether an analogous theory of calculus is possible for the next hyperoperation after multiplication, which is exponentiation. Peer-review this article by using the comments or upvoting/downvoting
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Seeing the Anatomy of Quantum Gravity Through Formula of Everything – Sotade Olusegun
The prior publication of “The Time Theory of the Universe” reveals the true nature of time as “electromagnetic speed of relativistic scaling” through formula of everything. The formula of everything, dt/dm = Um + 4m depicts relationship between “time and mass”, “time and energy” and “energy and mass” as inverse. This inverse relationship necessitates the
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The Time Theory of the Universe – Sotade Olusegun
“Time, a determinant of weather-invoking occurrence as heat or cold for transformation of matter into solid, liquid or gas at needed conditioning level explains why particle is an intrinsic property of matter which is wave or particle in behaviour as it navigates through its various forms in necessitated space of compactness for mass, densely spaced
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