Frequency Domain Modeling with Piecewise Constant Spectra

Modeling a Tumor Growth with Piecewise Constant Arguments

β 0 x(⟦t⟧) − β 1 x(⟦t − 1⟧)) + γ 1 x(⟦t⟧) + γ 2 x(⟦t − 1⟧)}, where the parameters α, β 0 , β 1 , and r denote positive numbers, γ 1 and γ 2 are negative numbers and ⟦t⟧ is the integer part of t ∈ [0,∞). Equation (A) explains a brain tumor growth, where γ 1 is embedded to show the drug effect on the tumor and γ 2 is a rate that causes a negative effect by the immune system on the tumor populatio...

Piecewise Constant Controlled Linear Fuzzy Systems

Adaptive Piecewise-constant Modeling of Signals in Multidimensional Spaces

This contribution describes an analysis method for the class of problems in which data elements – e.g. measurements, event detections, etc. – are distributed over some region of space and/or time, or other coordinates (e.g., energy, redshift, category), with the goal of estimating the variation of some physical quantity. The nonparametric model is simply that the physical variable is constant o...

Frequency-domain seismic modeling with the MUMPS

Seismic imaging has many applications in civil engineering, risk hazard, waste storage monitoring, oil exploration and tectonophysics. Among the different seismic imaging methods the full waveform inversion aims to exploit the full information content of seismic data through the complete resolution of the partial differential wave equation. Once the wave equation has been solved for each seismi...

Incompressible flows with piecewise constant density

We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous initial density. In dimension n = 2, 3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness h...