Thought/ visual processing: ctrl + x, y, z, v

With this text I wish to revisit a long-standing preoccupation of mine which addresses the extent to which the digital medium may have brought about a paradigm shift in creative process; one which has been effectuated through a conversion of the creative medium itself - from atoms to bits. As a visual practitioner, what is particularly significant to my inquiry is that this change in medium is deemed to have brought about a change in language that affects the very nature of autographic work which comes into being as visual output: Following Goodman’s definitions of allographic and autographic output (1976), McCullough (1996) asserts that visual artworks may now be considered to be allographic productions since they presently share the same attributes of notationally based allographic work, which has traditionally manifested only as music or as literary output. The result is a work environment which wide opens the doors to unprecedented levels of non-linear process and experimentation whilst engaged in the visually creative act

A note on Higgs decays into ZZ boson and J/Ψ(Υ)J/\Psi (\Upsilon)

Rare decays $h\to Z V$ with $V$ denoting the narrow $c\bar{c}$ or $b\bar{b}$ resonances, such as $J/\Psi$ or $\Upsilon$ states, have been analyzed. Within the standard model, these channels may proceed through the tree-level transition $h\to ZZ^*$ with the virtual $Z^*\to V$, and also loop-induced process $h\to Z\gamma^*$, followed by $\gamma^*\to V$. Our analysis shows that, for the bottomonium final states, the decay rate of $h\to Z \Upsilon$ from the loop-induced process is small and the former transition gives the dominant contribution; while, for the charmonium final states, $\Gamma(h\to Z J/\Psi)$ and $\Gamma(h\to Z\Psi(2S))$ induced by $h\to Z\gamma^* \to Z V$ could be comparable to the contribution given by the tree-level $h\to ZZ^*\to Z V$ transition.Comment: 6 pages, 2 figure

A connection between viscous profiles and singular ODEs

We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $$dV / dt = F(V) / z (V) .$$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth. The real valued function z is as well regular: the equation is singular in the sense that z (V) can attain the value 0.Comment: 6 pages, minor change

Alfvén 'resonance' reconsidered: Exact equations for wave propagation across a cold inhomogeneous plasma

Previous discussions of Alfvén wave propagation across an inhomogeneous plasma predicted that shear Alfvén waves become singular (resonant) at the omega = k(z)v(A) layer and that there is a strong wave absorption at this layer giving localized ion heating. In this paper the three standard derivations of the Alfvén 'resonance' (incompressible magnetohydrodynamics, compressible magnetohydrodynamics, and two-fluid) are re-examined and shown to have errors and be mutually inconsistent. Exact two-fluid differential equations for waves propagating across a cold inhomogeneous plasma are derived; these show that waves in an ideal cold plasma do not become 'resonant' at the Alfvén layer so that there is no wave absorption or localized heating. These equations also show that the real 'shear' Alfvén wave differs in substance from both the ideal MHD and earlier two-fluid predictions and, in the low density, high field region away from the omega = k(z)v(A) layer, is actually a quasielectrostatic resonance cone mode. For omega much-lesser-than omega(ci) and k(y) = 0, the omega = k(z)v(A) layer turns out to be a cutoff (reflecting) layer for both the 'shear' and compressional modes (and not a resonance layer). For finite omega/omega(ci) and k(y) = 0 this layer becomes a region of wave inaccessibility. For omega much-lesser-than omega(ci) and finite k(y) there is strong coupling between shear and compressional modes, but still no resonance

Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains

We prove that for a strongly pseudoconvex domain $D\subset\mathbb C^n$, the infinitesimal Carath\'eodory metric $g_C(z,v)$ and the infinitesimal Kobayashi metric $g_K(z,v)$ coincide if $z$ is sufficiently close to $bD$ and if $v$ is sufficiently close to being tangential to $bD$. Also, we show that every two close points of $D$ sufficiently close to the boundary and whose difference is almost tangential to $bD$ can be joined by a (unique up to reparameterization) complex geodesic of $D$ which is also a holomorphic retract of $D$. The same continues to hold if $D$ is a worm domain, as long as the points are sufficiently close to a strongly pseudoconvex boundary point. We also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed, this has consequences for the behavior of the squeezing function

Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains

We prove that for a strongly pseudoconvex domain $D\subset\mathbb C^n$, the infinitesimal Carath\'eodory metric $g_C(z,v)$ and the infinitesimal Kobayashi metric $g_K(z,v)$ coincide if $z$ is sufficiently close to $bD$ and if $v$ is sufficiently close to being tangential to $bD$. Also, we show that every two close points of $D$ sufficiently close to the boundary and whose difference is almost tangential to $bD$ can be joined by a (unique up to reparameterization) complex geodesic of $D$ which is also a holomorphic retract of $D$. The same continues to hold if $D$ is a worm domain, as long as the points are sufficiently close to a strongly pseudoconvex boundary point. We also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed, this has consequences for the behavior of the squeezing function

Tuples of polynomials over finite fields with pairwise coprimality conditions

Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v that satisfy given pairwise coprimality conditions. We show how this generalises from monic polynomials in finite fields to Dedekind domains with a finite norm