arXiv subjects
Publications and source records attributed to Richard Vale.
This note observes that the Cobb-Douglas function is uniquely characterized by the property that, if the labour share of cost for a constant-returns-to-scale firm remains constant when the firm minimizes its cost for any given output level, then the firm's production function must be Cobb-Douglas.
Many large and small companies in the tech and startup sector have been laying off an unusually high number of workers in 2022 and 2023. We are interested in predicting when this period of layoffs might end, without resorting to economic forecasts. We observe that a sample of layoffs up to March 31, 2023 follow the pattern of noisy observations from an SIR (Susceptible-Infectious-Removed) model. A model is fitted to the data using an analytical solution to the SIR model obtained by Kr\"{o}ger and Schlickeiser. From the fitted model we estimate that the number of weekly layoffs will return to normal levels around the end of 2023.
We present a discrete-time dynamic model of income tax evasion. The model is solved exactly in the case of a single taxpayer and shown to have some realistic properties, including avoiding the Yitzhaki paradox. The extension to an agent-based model with a network of taxpayers is also investigated.
Predictions are made for the number of chapters told from the point of view of each character in the next two novels in George R. R. Martin's \emph{A Song of Ice and Fire} series by fitting a random effects model to a matrix of point-of-view chapters in the earlier novels using Bayesian methods. {\textbf{SPOILER WARNING: readers who have not read all five existing novels in the series should not read further, as major plot points will be spoiled.}}
We describe which topological spaces can arise as the prime spectrum of a commutative monoid, in the spirit of Hochster's and Brenner's theses.
We define a faithful contravariant functor NCSpec from the category of rings to the category of ringed spaces, and show that if R is a commutative ring then NCSpec(R) may be viewed as a completion of Spec(R) in an appropriate sense. We then explain how the spaces NCSpec(R) may be glued, and study quasicoherent sheaves on them. As an example, we compute the category of quasicoherent sheaves on a space constructed from a skew-polynomial ring R by an analogue of the Proj construction.
We determine the structure of category $\cO$ for the rational Cherednik algebra of $G(m,1,n)$ in the case where the $\KZ$ functor satisfies a condition called \emph{separating simples}. As a consequence, we show that the property of having exactly $N-1$ simple modules, where $N$ is the number of simple modules of $G(m,1,n)$, determines the Ariki-Koike algebra up to isomorphism.
We construct a quotient ring of the ring of diagonal coinvariants of the complex reflection group $W=G(m,p,n)$ and determine its graded character. This generalises a result of Gordon for Coxeter groups. The proof uses a study of category $\cO$ for the rational Cherednik algebra of $W$.