Search results for "singular"

A numerical meshless particle method in solving the magnetoencephalography forward problem

2012

In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell's curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless…

Frequency-Sliding Generalized Cross-Correlation: A Sub-Band Time Delay Estimation Approach

2020

The generalized cross correlation (GCC) is regarded as the most popular approach for estimating the time difference of arrival (TDOA) between the signals received at two sensors. Time delay estimates are obtained by maximizing the GCC output, where the direct-path delay is usually observed as a prominent peak. Moreover, GCCs play also an important role in steered response power (SRP) localization algorithms, where the SRP functional can be written as an accumulation of the GCCs computed from multiple sensor pairs. Unfortunately, the accuracy of TDOA estimates is affected by multiple factors, including noise, reverberation and signal bandwidth. In this paper, a sub-band approach for time del…

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

2014

Monitoring the dynamics of protonation and protein backbone conformation changes during the function of a protein is an essential step towards understanding its mechanism. Protonation and conformational changes affect the vibration pattern of amino acid side chains and of the peptide bond, respectively, both of which can be probed by infrared (IR) difference spectroscopy. For proteins whose function can be repetitively and reproducibly triggered by light, it is possible to obtain infrared difference spectra with (sub)microsecond resolution over a broad spectral range using the step-scan Fourier transform infrared technique. With -10(2)-10(3) repetitions of the photoreaction, the minimum num…

Riesz transform and vertical oscillation in the Heisenberg group

2023

We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, and Young, we first introduce new scale and translation invariant coefficients $\operatorname{osc}_{\Omega}(B(q,r))$. These coefficients quantify the vertical oscillation of a domain $\Omega \subset \mathbb{H}$ around a point $q \in \partial \Omega$, at scale $r > 0$. We then proceed to show that if $\Omega$ is a domain bounded by an intrinsic Lipschitz graph $\Gamma$, and $$\int_{0}^{\infty} \operatorname{osc}_{\Omega}(B(q,r)) \, \frac{dr}{…

The Bochner and Riesz integral representations for the Radon transform

1984

Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method

2009

Abstract In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials . The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method . The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation σ − Δ u that describes the interaction between mechanical and kinematical quantities…

New techniques for classification of multigerms

2018

Abstract The goal of these notes is to give an overview of the state of the art in classification of multigerms. We have tried to make them self-contained but certainly not extensive. The results included here scope most of the research on classification of multigerms carried out in the last 15 years with special emphasis on recent results by the authors of these notes and their collaborators.

General Theory: Algebraic Point of View

2009

It is convenient to divide our study of pip-spaces into two stages. In the first one, we consider only the algebraic aspects. That is, we explore the structure generated by a linear compatibility relation on a vector space V , as introduced in Section I.2, without any other ingredient. This will lead us to another equivalent formulation, in terms of particular coverings of V by families of subspaces. This first approach, purely algebraic, is the subject matter of the present chapter. Then, in a second stage, we introduce topologies on the so-called assaying subspaces \(\{V_r \}\). Indeed, as already mentioned in Section I.2, assuming the partial inner product to be nondegenerate implies tha…

Families of Two-dimensional Vector Fields

1998

In this section we will consider individual vector fields. They can be considered as 0-parameter families. We assume these vector fields to be of class at least C 1. This will be sufficient to ensure the existence and uniqueness of the flow φ(t, x) (t is time, x ∈ S, the phase space) and the qualitative properties which we mention below.

Bifurcations of Regular Limit Periodic Sets

1998

In this chapter, (X λ ) will be a smooth or analytic (in Section 3) family of vector fields on a phase space S, with parameter λ ∈ P, as in Chapter 1. Periodic orbits and elliptic singular points which are limits of sequences of limit cycles are called regular limit periodic sets. The reason for this terminology is that for such a limit periodic set Γ one can define local return maps on transversal segments, which are as smooth as the family itself. The limit cycles near Γ will be given by a smooth equation and the theory of bifurcations of limit cycles from Γ will reduce to the theory of unfoldings of differentiable functions. In fact, we will just need the Preparation Theorem and not the …