First we give a truly short proof of the major blow up result [Si] on higher dimensional semilinear wave equations. Using this new method, we also establish blow up phenomenon for wave equations with a potential. This complements the recent interesting existence result by [GHK], where the blow up problem was left open.

SWAS: A shear-wave analysis system for semi-automatic measurement of shear-wave splitting above small earthquakes Yuan Gao a,b, Ping Hao a, Stuart Crampin a,b,c,∗ a Institute of Earthquake Science, China Earthquake Administration, 100036 Beijing, China b School of GeoSciences, University of Edinburgh, Edinburgh EH9 3JW, Scotland, UK c Edinburgh Anisotropy Project, British Geological Survey, Edi...

Citation Coates, A. S., E. P. Winer, A. Goldhirsch, R. D. Gelber, M. Gnant, M. Piccart-Gebhart, B. Thürlimann, and H.-J. Senn. 2015. “Tailoring therapies—improving the management of early breast cancer: St Gallen International Expert Consensus on the Primary Therapy of Early Breast Cancer 2015.” Annals of Oncology 26 (8): 1533-1546. doi:10.1093/annonc/mdv221. http://dx.doi.org/10.1093/annonc/md...

Debate over the consequences of marine reserve implementation has long focused on tradeoffs between ecological improvements from reserves and possible economic losses from reduced harvest. More recently, several articles suggest instead that reserves might generate economic as well as ecological benefits (1; 2; 3; 4). In particular Hastings and Botsford demonstrate that, even without any ecolog...

We present the universal two-loop splitting functions that describe the limits of two-loop n-point amplitudes of massless particles when two of the momenta are collinear. To derive the splitting amplitudes, we take the collinear limits of explicit two-loop four-point helicity amplitudes computed in the ’t Hooft-Veltman scheme. The g → gg splitting amplitude has recently been computed using the ...

We study 3-valent maps Mn(p, q) consisting of a ring of n q-gons whose the inner and outer domains are filled by p-gons, for p, q ≥ 3. We describe a domain in the space of parameters p, q, and n, for which such a map may exist. With four infinite sequences of maps prisms Mp(p ≥ 3, 4), M4(4, q ≥ 4), M4(5, 5t+2 ≥ 7), M4(5, 5t+3 ≥ 8), we give 26 sporadic ones. The maps whose p-gons form two paths ...

In this paper, we show that all the coordinate functions of the Advanced Encryption Standard (AES) round function are equivalent under an aane transformation of the input to the round function. In other words, let fi and fj be any two distinct output coordinates of the AES round function, then there exists a nonsingular matrix Aji over GF(2) such that fj(Ajix) + bji = fi(x); bji 2 GF(2). We als...

We study metrics on the shape space of curves that induce a prescribed splitting of the tangent bundle. More specifically, we consider reparametrization invariant metrics G on the space Imm(S,R) of parametrized regular curves. For many metrics the tangent space TcImm(S ,R) at each curve c splits into vertical and horizontal components (with respect to the projection onto the shape space Bi(S ,R...