we discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of kirchhoff type [ u_{tt}-phi (x)||nabla u(t)||^{2}delta u+delta u_{t}=|u|^{a}u,, x in mathbb{r}^{n} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $n geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $l^{n/2}(mathb...

Many audio and multimedia applications would benefit from the ability to classify and search for audio based on its characteristics. The audio analysis, search, and classification engine described here reduces sounds to perceptual and acoustical features. This lets users search or retrieve sounds by any one feature or a combination of them, by specifying previously learned classes based on thes...

The dynamics of the 4-body problem allows for two binary collisions to occur simultaneously. It is known that in collinear this simultaneous collision (SBC) can be block-regularised, but resulting block map only $C^{8/3}$ differentiable. In paper, it proved differentiability persists SBC planar problem. proof uses several geometric tools, namely, blow-up, normal forms, near normally hyperbolic ...