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The general context for a symmetry- based analysis of pattern formation in equivariant dynamical systems is sym- metric (or equivariant) bifurcation theory.. This is surveyed
Several other generalizations of compositions have appeared in the literature in the form of weighted compositions [6, 7], locally restricted compositions [3, 4] and compositions
Analogs of this theorem were proved by Roitberg for nonregular elliptic boundary- value problems and for general elliptic systems of differential equations, the mod- ified scale of
Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A
Definition An embeddable tiled surface is a tiled surface which is actually achieved as the graph of singular leaves of some embedded orientable surface with closed braid
Correspondingly, the limiting sequence of metric spaces has a surpris- ingly simple description as a collection of random real trees (given below) in which certain pairs of
[Mag3] , Painlev´ e-type differential equations for the recurrence coefficients of semi- classical orthogonal polynomials, J. Zaslavsky , Asymptotic expansions of ratios of
p≤x a 2 p log p/p k−1 which is proved in Section 4 using Shimura’s split of the Rankin–Selberg L -function into the ordinary Riemann zeta-function and the sym- metric square