Mathematics

  2010 MAR 9 - (VerticalNews.com) -- "We study Fredholm determinants related to a family of kernels that describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher-order analogues of the Airy kernel and are built out of functions associated with the Painleve I hierarchy," scientists writing in the journal Communications on Pure and Applied Mathematics report ...read more

  2010 MAR 9 - (VerticalNews.com) -- "The following first problem is posed - to justify that the standing shock wave S-(x) = -sign x ={-1 for x< 0, 1 for x> 0 F6 r x< 0, is a correct 'entropy solution' of the Cauchy problem for the fifth-ordcr degenerate non-linear dispersion equations (NDEs), as for the classic Euler one u(1) + uu(x) = 0, u(1) = -(uu(x))(xxxx) and u(1) = -(uu(xxx))(x) m R x R+. These two quasi-linear degenerate partial differential equations (PDEs) arc chosen as typical representatives, so other (2m + 1)th-order NDEs of non-divergent form admit such shocks waves," scientists writing in the European Journal of Applied Mathematics report ...read more

  2010 MAR 9 - (VerticalNews.com) -- "This work considers longitudinal wave propagation in circular cylindrical rods adopting Bostrom's power series expansion method in the radial coordinate. Equations of motion together with consistent sets of general lateral and end boundary conditions are derived in a systematic fashion up to arbitrary order using a generalized Hamilton's principle," scientists writing in the Quarterly Journal of Mechanics and Applied Mathematics report ...read more