We present a new solution for the dispersive element in astronomical spectrographs, which in many cases can provide an upgrade path to enhance the spectral resolution of existing moderate-resolution reflection-grating spectrographs. We demonstrate that in the case of LRIS-R at the Keck 1 Telescope a spectral resolution of 18,000 can be achieved with reasonable throughput under good seeing condi...

We prove dispersive estimates for solutions to the Schrödinger equation with a real-valued potential V ∈ L∞(R), n ≥ 4, satisfying V (x) = O(〈x〉−(n+2)/2−ǫ), ǫ > 0.

We prove dispersive estimates at low frequency in dimensions n ≥ 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance. This class includes potentials V ∈ L∞(R) satisfying V (x) = O ( 〈x〉−(n+1)/2−ǫ ) , ǫ > 0.

We estimate the di-photon coupling of f0(600), f0(980) and f2(1270) resonances in a couple channel dispersive approach. Especially we estimate the di-photon coupling of the third sheet pole located near K̄K threshold, denoted as f III 0 (980). It is argued that this third sheet pole may be originated from a couple channel Breit-Wigner description of the f0(980) resonance. The f0(600) di-photon c...

Article history: Received 11 October 2013 Received in revised form 14 July 2014 Accepted 19 August 2014 Available online 28 August 2014

in this paper, we obtain a suitable mathematical model for the seismic response of dams. by using the shear beam model (sb model), we give a mathematical formulation that it is a partial differential equation and transform it to the sturm-liouville equation.

and Applied Analysis 3 Subject to the initial condition D α−k 0 U (x, 0) = f k (x) , (k = 0, . . . , n − 1) , D α−n 0 U (x, 0) = 0, n = [α] , D k 0 U (x, 0) = g k (x) , (k = 0, . . . , n − 1) , D n 0 U (x, 0) = 0, n = [α] , (11) where ∂α/∂tα denotes the Caputo or Riemann-Liouville fraction derivative operator, f is a known function, N is the general nonlinear fractional differential operator, a...

We discuss the general theoretical ideas of the possibility using cryptosystems based on the partial differential equations (PDE) and the role of inverse scattering problem for the cryptanalysis as the possible way to the postquantum cipher scheme. An application of the nonlinear Schrödinger equation and optical fibre technology in cryptology is presented.

This article concerns the dressing method for solving of multidimensional nonlinear Partial Differential Equations. In particular, we join hierarchy of matrix Burgers type equation with hierarchies of equations integrable by the Inverse Spectral Transform (IST). Example of resonance interaction of wave packets in (3+1)-dimensions is given.

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.