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One unaddressed challenge in optical metrology has been the measurement of higher order derivatives of rough specimens subjected to loading. In this paper, we investigate an approach that allows for the simultaneous estimation of the phase and its higher o ...
The large sieve inequalities for algebraic trace functions are considered in this article. A fundamental iterative relation is established by classical Fourier analysis, and l-adic Fourier analysis and multiplicative convolutions of sheaves are also requir ...
In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...
Real-Time Optimization (RTO) via modifier adaptation is a class of methods for which measurements are used to iteratively adapt the model via input-affine additive terms. The modifier terms correspond to the deviations between the measured and predicted co ...
We discuss Lp integrability estimates for the solution u of the advection–diffusion equation ∂tu+div(bu)=Δu, where the velocity field b∈LtrLxq. We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Af ...
We report a new technique for the demodulation of a closed fringe pattern by representing the phase as a weighted linear combination of a certain number of linearly independent Fourier basis functions in a given row/column at a time. A state space model is ...
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” ...
The increasing availability of network data is leading to a growing interest in processing of signals on graphs. One notable tool for extending conventional signal-processing operations to networks is the graph Fourier transform that can be obtained as the ...
Institute of Electrical and Electronics Engineers2016
This project offers a rigorous introduction to the tools needed to construct a continuous stochastic process. Among other things, we give a very detailed proof of the Kolmogorov continuity criterion. We then construct a Brownian Motion following the formal ...
Let Omega be a bounded domain of R-N (N >= 2). We obtain a necessary and a sufficient condition, expressed in terms of capacities, for the existence of a solution to the porous medium equation with absorption {u(t) - Delta (vertical bar u vertical bar(m-1) ...