[4] viXra:2309.0115 [pdf] submitted on 2023-09-23 04:06:52
Authors: Ryan J. Buchanan, Parker Emmerson, Oliver Hancock
Comments: 7 Pages.
We model an absolute reference frame using a pullback on a certain locally trivial line bundle. We demonstrate that this pullback is unrealizable in $mathbb{R}^4$. We devote section 3 to process-based thinking.
Category: Set Theory and Logic
[3] viXra:2309.0053 [pdf] submitted on 2023-09-09 23:39:25
Authors: Ryan J. Buchanan
Comments: 3 Pages. (Abstract added by viXra Admin - Please conform!)
Factions, or agent-based secret-sharing networks, are discussed. Convergence of multiple belief systems is described as the anisotropic propagation of truth by factions.
Category: Set Theory and Logic
[2] viXra:2309.0029 [pdf] submitted on 2023-09-04 07:41:17
Authors: Ryan J. Buchanan
Comments: 3 Pages.
Lawvere introduced a deceptively simple category, V, which is complete, symmetric, and monoidal closed. Here, we extend this construction to describe a rather general notion of localization called -truncation. We show that this procedure produces tame, realizable n-cells in a standard Grothendieck universe, . Finally, we clarify our notion of smallness for objects of stable rings in .
Category: Set Theory and Logic
[1] viXra:2309.0028 [pdf] submitted on 2023-09-05 03:14:24
Authors: Kum-Chol Son, Song Jin-A, Ro Song-Chol
Comments: 20 Pages.
We introduce new concepts-a generator of degree and a diagonal section of degree for any real number . A diagonal section of degree is the one of the bivariate Archimedean copula with a generator of degree . Generators of many well-known parametric families of bivariate Archimedean copulas, including those of Clayton, Frank and Gumbel-Hougaard, are of degree . In this article, we show that each bivariate Archimedean copula with a generator of degree is uniquely determined by its diagonal section. An asymptotic representation of these copulas in terms of corresponding diagonal sections is obtained. We also provide a sufficient condition to be a diagonal section of degree . These results allow us to construct several statistical inference procedures for bivariate Archimedean copulas. Since diagonal sections of copulas are absolutely continuous, we suggest a parametric estimation procedure for bivariate Archimedean copulas based on the likelihood of a full sample from the diagonal section.
Category: Set Theory and Logic