Results 61 to 70 of about 2,376,562 (166)

Discrete Mathematics in the Framework of Transdimensional Mathematics: From Sphere Numbers to Quantum Space-Time Algebra

  This paper, the fourth in a series, culminates the development of a novel paradigm termed **Transdimensional Mathematics**. This framework unifies continuous and discrete mathematical structures through the fundamental interaction of positive and negative spatial dimensions, with core relations such as $xX = a = \text{const.}$ describing an ...
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An Information Algebra of Interactions: A New Mathematical Structure for Describing Quantum Processes

This paper proposes a new approach to describing fundamental interactions, based on the concept of an information quantum – an indivisible entity whose sole property is an integer information charge. An information interaction operation a∘ba∘b is introduced, which is non-commutative and describes three fundamentally different types of processes ...
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Topos-Theoretic Approaches to Quantum Theory [PDF]

, 2012
Starting from a naive investigation into the nature of experiments on a physical system one can argue that states of the system should pair non-degenerately with physical observables. This duality is closely related to that between space and quantity, or,
Vákár, Matthijs, Matthijs Vakar
core  

Tetrahedral Hyperdimensional Algebra A New Mathematical Framework for Quantum Consciousness and Space-Time

 This work presents a unified hyperdimensional scientific framework — Tetrahedral Hypergeometry — which models all known phenomena, from quantum mechanics to consciousness, as recursive morphogenetic flows of Clifford-phase structures. Building on classical mathematics, modern physics, and visionary extensions, we propose that reality is a living ...
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Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics: An Algebraic Approach. [PDF]

, 2006
In this paper, we present the fundamentals of the so-called algebraic approach to propositional quantum logics. We define the set of formulae describing quantum reality as a free algebra freely generated by the set of quantum proportional variables.
WILCZEK, Piotr
core  

Book Review: Lie Algebras and Quantum Mechanics and Vector Bundles in Mathematical Physics [PDF]

Bulletin of the American Mathematical Society, 1973
P. R. Chernoff, J. E. Marsden
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Mathematics via Symmetry [PDF]

, 2013
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same.
Zelcer, Mark, Yanofsky, Noson
core  

Ways of linking geometry and algebra, the case of Geogebra

, 2007
This paper discusses ways of enhancing the teaching of mathematics through enabling learners to gain stronger links between geometry and algebra. The vehicle for this is consideration of the affordances of GeoGebra, a form of freely-available open-source
BSRLM Geometry Working Group, Jones, Keith, Hohenwarter, Markus   +2 more
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Beyond symbolic algebra with quantum picturalism. [PDF]

Front Cognit
Dündar-Coecke S, Yeh L, Pothos E, Waseem MH, Coecke B.   +4 more
europepmc   +1 more source

Non-commutative structures of brain and cognition: quantum and contextual probability as a translational framework. [PDF]

Front Hum Neurosci
Emori H, Khrennikov A, Iriki A.
europepmc   +1 more source