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Higher-Dimensional Twistor Transforms using Pure Spinors
Hughston has shown that projective pure spinors can be used to construct
massless solutions in higher dimensions, generalizing the four-dimensional
twistor transform of Penrose. In any even (Euclidean) dimension d=2n,
projective pure spinors parameterize the coset space SO(2n)/U(n), which is the
space of all complex structures on R^{2n}. For d=4 and d=6, these spaces are
CP^1 and CP^3, and the appropriate twistor transforms can easily be
constructed. In this paper, we show how to construct the twistor transform for
d>6 when the pure spinor satisfies nonlinear constraints, and present explicit
formulas for solutions of the massless field equations.Comment: 17 pages harvmac tex. Modified title, abstract, introduction and
references to acknowledge earlier papers by Hughston and other
Studies on generalized Yule models
We present a generalization of the Yule model for macroevolution in which,
for the appearance of genera, we consider point processes with the order
statistics property, while for the growth of species we use nonlinear
time-fractional pure birth processes or a critical birth-death process.
Further, in specific cases we derive the explicit form of the distribution of
the number of species of a genus chosen uniformly at random for each time.
Besides, we introduce a time-changed mixed Poisson process with the same
marginal distribution as that of the time-fractional Poisson process.Comment: Published at https://doi.org/10.15559/18-VMSTA125 in the Modern
Stochastics: Theory and Applications (https://vmsta.org/) by VTeX
(http://www.vtex.lt/
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