In 1962, the historian A. B. L. Awasthi wrote, “the Turkish conquest of India began with the Arab conquest of Sind.” The sentiment expresses a common teleology according to which Muslims, irregardless of their ethnicity, linguistic identities, or specific sectarian affiliations, acted in concert across more than five centuries to affect a “slow progress of Islamic power” in South Asia as D. R. ...

Here it is shown that chaotic oscillations can appear after a series of period doublings in radiating diffusion flames when the activation temperature is high enough. It is also shown that period doubling cascades appear typically in very small regions and that they may not be observable if one starts with small perturbations of a steady flame.

We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...

We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...

In this paper, we study the linear structure of sets A ⊂ Fn2 with doubling constant σ(A) < 2, where σ(A) := |A+A| |A| . In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with |V | ≤ |A|. Finally, we classify all binary sets with small doubling constant.

We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν, where the Borel measure ν satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When ν = f dx, this condition, which we call D , admits the possibility of f vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when 0 < ...

Ilias Kazanis,1* Justin D. Lathia,1,2* Tegy J. Vadakkan,3 Eric Raborn,4,5,6 Ruiqian Wan,2 Mohamed R. Mughal,2 D. Mark Eckley,7 Takako Sasaki,8 Bruce Patton,9 Mark P. Mattson,2 Karen K. Hirschi,4,5,6 Mary E. Dickinson,3 and Charles ffrench-Constant1,10 1Department of Pathology, University of Cambridge, Cambridge CB2 1QP, United Kingdom, 2Laboratory of Neurosciences, National Institute on Aging I...

Disclosure: Mario Castro has received research support from NIH, ALA, CDC, Amgen, Boston Scientific, Boehringer Ingelheim, Cephalon, Genentech, GSK, Invion, Johnson & Johnson, Kalobios, MedImmune, NextBio, Novartis, Sanofi Aventis, and Vectura. He is on the lecture bureau for Boehringer Ingelheim, Boston Scientific, Genentech, GSK, and Teva. He has acted as consultant for Boston Scientific, Gal...