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.

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...

Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differen...

nonstandard finite difference schemes for the black-scholes partial differential equation preserving the positivity property are proposed. computationally simple schemes are derived by using a nonlocal approximation in the reaction term of the black-scholes equation. unlike the standard methods, the solutions of new proposed schemes are positive and free of the spurious oscillations.