in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims prediction and prediction uncertainty for the Munich chain-ladder method in a consistent way.

We propose a modified version of the chaotic cryptographic method based on iterating a logistic map. Simulation results show that the distribution of the ciphertext is flatter and the encryption time is shorter. Moreover, the trade-off between the spread of the distribution of ciphertext and the encryption time can be controlled by a single parameter.  2001 Elsevier Science B.V. All rights res...

The article (1) by Gancedo and Strain in PNAS studies how singularities may develop in the initially smooth interfaces separating two or more incompressible fluids. The fluids and interfaces are assumed to evolve by either of the two standard systems of equations from fluid mechanics, namely the surface quasi-geostrophic (SQG) sharp front equation (2) or the Muskat equation (3). Gancedo and Str...

Article history: Received 30 December 2014 Accepted 13 August 2015 Available online xxxx Communicated by Charles Fefferman MSC: 35R35 35Q35 35S10 76B03

We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy’s law. We establish that as long as the slope of the interface between the two fluids remains bounded and uniformly continuous, the solution remains regular. The proofs exploit the nonlocal nonlinear parabolic nature of the equations through a...

1 Japan Atomic Energy Agency, 2-4 Shirakata, Tokai-mura, Ibaraki, 319-1195, Japan 2 Oita Prefecture-Mie Hospital, 3964-1 Miemachi-Miyano, Bungoono-shi, Oita, 879-7101, Japan 3 Shin-Beppu Hospital, 3898 Tsurumi, Beppu-shi, Oita, 874-0833, Japan 4 Tokai University Oiso Hospital, 21-1 Gakkyou, Oiso-machi, Kanagawa, 259-0198, Japan 5 Tokai University Hospital, 143 Shimokasuya, Isehara-shi, Kanagawa...