Studies In Applied Mathematics

@inproceedings{Taub1971StudiesIA,
  title={Studies In Applied Mathematics},
  author={A. H. Taub},
  year={1971}
}
New approaches to coding information using inverse scattering transform
TLDR
This work proposes to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design, and introduces a soliton orthogonal frequency division multiplexing (SOFDM) method based on the choice of identical imaginary parts of the N-soliton solution eigenvalues.
Non-classical symmetries and the singular manifold method: a further two examples
This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the
Exact solutions for one of the extensive chaos model
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions
Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation
In this paper, we have studied the geometrical formulation of the Landau-Lifshitz equation (LLE) and established its geometrical equivalent counterpart as some generalized nonlinear Schrödinger
Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
TLDR
A Rogue Wave Detection Network (RWD-Net) model is proposed to automatically and accurately detect RWs on the images, which directly indicates they have the similar computer vision patterns.
Quantifying Health Inequalities Induced by Data and AI Models
TLDR
A generic allocation-deterioration framework for detecting and quantifying AI induced inequality and showing its ability to accurately detect and quantify inequality proportionally to controlled inequalities is proposed.
Dark solitons of the Gross-Neveu model
We present N-soliton solutions for the classical (1+1)-dimensional Gross–Neveu model which satisfy non-zero boundary conditions. These solutions are obtained by direct method using some properties of
Stochastic Wave-Current Interaction in Thermal Shallow Water Dynamics
TLDR
In the entire family of nonlinear stochastic wave-current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.
Determining Asymptotic Stability and Robustness of Networked Systems
TLDR
A novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions is presented.
Residual-type a posteriori error estimator for a quasi-static Signorini contact problem
  • M. Walloth
  • Mathematics
    IMA Journal of Numerical Analysis
  • 2019
We present a new residual-type a posteriori estimator for a quasi-static Signorini problem. The theoretical results are derived for two- and three-dimensional domains and the case of nondiscrete
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