The main results of this paper are concerned with the “bad” behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class C2 in any Sobolev space.

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) order ϰ∈(0,1) using Picard iteration technique (PIT) semimartingale local time (SLT).

We propose a novel second order in time numerical scheme for Cahn-Hilliard-NavierStokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, ...

Accurate and efficient orbital propagators are critical for space situational awareness because they drive uncertainty propagation which is necessary for tracking, conjunction analysis, and maneuver detection. We have developed an adaptive, implicit Runge-Kuttabased method for orbit propagation that is superior to existing explicit methods, even before the algorithm is potentially parallelized....

A computationally simple, numerical algorithm capable of solving a wide variety of twodimensional, variably saturated flow problems is developed. Recent advances in modeling variably saturated flow are incorporated into the algorithm. A physically based form of the general, variably saturated flow equation is solved using finite differences (centered in space, fully implicit in time) employing ...

Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for function has recently become a powerful tool for understanding how evolution can innovate within its genetic rule space. However, conventional cel...

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

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...