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Elemental Principles Of T-Topos, Goro Kato
Elemental Principles Of T-Topos, Goro Kato
Mathematics
In this paper, a sheaf-theoretic approach toward fundamental problems in quantum physics is made. For example, the particle-wave duality depends upon whether or not a presheaf is evaluated at a specified object. The t-topos theoretic interpretations of double-slit interference, uncertainty principle(s), and the EPR-type non-locality are given. As will be explained, there are more than one type of uncertainty principle: the absolute uncertainty principle coming from the direct limit object corresponding to the refinements of coverings, the uncertainty coming from a micromorphism of shortest observable states, and the uncertainty of the observation image. A sheaf theoretic approach …
Shallow Water Modeling Of Antarctic Bottom Water Crossing The Equator, Paul F. Choboter, Gordon E. Swaters
Shallow Water Modeling Of Antarctic Bottom Water Crossing The Equator, Paul F. Choboter, Gordon E. Swaters
Mathematics
The dynamics of abyssal equator-crossing flows are examined by studying simplified models of the flow in the equatorial region in the context of reduced-gravity shallow water theory. A simple “frictional geostrophic” model for one-layer cross-equatorial flow is described, in which geostrophy is replaced at the equator by frictional flow down the pressure gradient. This model is compared via numerical simulations to the one-layer reduced-gravity shallow water model for flow over realistic equatorial Atlantic Ocean bottom topography. It is argued that nonlinear advection is important at key locations where it permits the current to flow against a pressure gradient, a mechanism …
Constructing Random Probability Distributions, Theodore P. Hill, David E.R. Sitton
Constructing Random Probability Distributions, Theodore P. Hill, David E.R. Sitton
Research Scholars in Residence
This article surveys several classes of iterative methods for constructing random probability distributions (or random convex functions, or random homeomorphisms), and includes illustrative applications in statistics, optimal-control theory, and game theory. Computer simulations of these methods are fast and easy to implement