in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

We show that the measure on markings of Zn, d ≥ 3, with elements of {0,1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1 2 Tcov(Z d n). As a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter gr...

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...

The Kuramoto model (KM) of coupled phase oscillators on complete, Paley, and Erdős-Rényi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER graphs share many structural properties. For instance, they exhibit the same asymptotics of the edge distributions, homomorphism densities, graph spectra, and have constant graph limits. Nonetheless, we show that the as...

CALEY M. ORR,*' LUCAS K. DELEZENE,' JEREMIAH E. SCOTT,' MATTHEW W. TOCHERI,' and GARY T. SCHWARTZ,; 1 School of Human Evolution and Social Change, Arizona State University, Tempe, Arizona 85287-2402, USA, [email protected]; institute of Human Origins, Arizona State University, Tempe, Arizona 85287-4101, U.S.A.; Human Origins Program, Smithsonian National Museum of Natural History, Washington, D...

We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group Sn and are consistent as n varies. The extreme infinitely spherically symmetric permutation-valued processes are identified for the Hamming, Kendall-tau and Caley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity. MSC:

We present general principles for the preservation of a.c. spectrum under weak perturbations. The Schrödinger operators on the strip and on the Caley tree (Bethe lattice) are considered. In this paper, we consider the problem of preservation of a.c. spectrum for Schrödinger operators when the perturbation (potential) is decaying slowly at infinity. In a recent years, lots of results in this dir...

BACKGROUND Caley Pea (Lathyrus hirsutus) is potentially toxic to horses, but large case series are not reported. OBJECTIVES To describe the clinical signs of horses intoxicated with Lathyrus hirsutus and speculate on the neuroanatomical lesion localization and pathogenesis based upon the observed clinical signs. ANIMALS Twenty-two of 25 horses ranging in age from 6 to 34 months were affecte...