Search results for "Weight function"
showing 10 items of 20 documents
Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds
2003
For appropriate triples (M, g, M), where M is an (in general non-compact) manifold, g is a metric on T*M, and M is a weight function on T* M, we developed in [5] a pseudo-differential calculus on.A.4 which is based on the S(M, g)-calculus of L. Hormander [30] in local models. Here we prove that the algebra of operators of order zero is a submultiplicative Ψ*-algebra in the sense of B. Gramsch [21] in \( \mathcal{L}\left( {{L^2}\left( M \right)} \right)\). For the basic calculus we generalized the concept of E. Schrohe [40] of so-called SG-compatible manifolds. In the proof of the existence of “order reducing operators” we apply a method from [4], and the proof of spectral invariance and sub…
A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities
2013
The aim of this research is the development of a space-time driscretization method based on Diffuse Approximation Meshless method. This method, devoted to transient heat transfer problems presenting high temporal discontinuities, avoids any Finite-Difference time stepping procedure. The space-time discretization proposed here seems to be convenient for continuous transient heat transfer. Nevertheless, for problems including temporal discontinuities, some spurious oscillations, whose amplitudes depend on source power, appear. A new weight function respecting the principle of causality, based on a modification of the involved node’s selection and a normalisation of the distances, is developed…
On Multiresolution Transforms Based on Weighted-Least Squares
2014
This work is devoted to construct Harten’s multiresolution transforms using Weighted-Least squares for different discretizations. We establish a relation between the filters obtained using some decimation operators. Some properties and examples of filters are presented.
Expected principal stress directions under multiaxial random loading. Part II: Numerical simulation and experimental assessment through the weight fu…
1999
In Part I of the present work, the theoretical aspects of a proposed procedure to determine the expected principal stress directions under multiaxial random loading have been discussed. This procedure consists of averaging the instantaneous values of the three Euler angles through weight functions. In Part II here, a numerical simulation is presented to illustrate the above theoretical method. As an example, the algorithm proposed is applied to some experimental biaxial in- and out-of-phase stress states to assess the correlation between the expected principal stress directions and the position of the experimental fatigue fracture plane for such tests.
ω-hypoelliptic differential operators of constant strength
2004
Abstract We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in E ω (Ω) which is homogeneous ω-hypoelliptic is also σ-hypoelliptic for any weight function σ=O(ω). We also present a sufficient condition in order to ensure that a differential operator admits a parametrix and, as a consequence, we obtain some conditions on the weights (ω,σ) to conclude that, for any operator P(x,D) with constant strength, the σ-hypoellipticity of the frozen operator P(x0,D) implies the ω-hypoellipticity of P(x,D). This requires the use of pseudodifferential operators.
On Approximate Jumbled Pattern Matching in Strings
2011
Given a string s, the Parikh vector of s, denoted p(s), counts the multiplicity of each character in s. Searching for a match of a Parikh vector q in the text s requires finding a substring t of s with p(t) = q. This can be viewed as the task of finding a jumbled (permuted) version of a query pattern, hence the term Jumbled Pattern Matching. We present several algorithms for the approximate version of the problem: Given a string s and two Parikh vectors u, v (the query bounds), find all maximal occurrences in s of some Parikh vector q such that u <= q <= v. This definition encompasses several natural versions of approximate Parikh vector search. We present an algorithm solving this problem …
The weight function for charges - A rigorous theoretical concept for Kelvin probe force microscopy
2016
A comprehensive discussion of the physical origins of Kelvin probe force microscopy (KPFM) signals for charged systems is given. We extend the existing descriptions by including the openloop operation mode, which is relevant when performing KPFM in electrolyte solutions. We define the contribution of charges to the KPFM signal by a weight function, which depends on the electric potential and on the capacitance of the tip-sample system. We analyze the sign as well as the lateral decay of this weight function for different sample types, namely, conductive samples as well as dielectric samples with permittivities both larger and smaller than the permittivity of the surrounding medium. Dependin…
Imaging Static Charge Distributions: A Comprehensive KPFM Theory
2018
We analyze Kelvin probe force microscopy (KPFM) for tip-sample systems that contain static charges by presenting a rigorous derivation for the respective KPFM signal in all common KPFM modes, namely amplitude modulation, frequency modulation, or heterodyne detection in the static, open-loop or closed-loop variant. The electrostatic model employed in the derivation is based on a general electrostatic analysis of an arbitrary tip-sample geometry formed by two metals, and which can include a static charge distribution and dielectric material in-between. The effect of the electrostatic force on the oscillating tip is calculated from this model within the harmonic approximation, and the observab…
The threshold behaviour of partial wave scattering amplitudes and theN/D-method
1964
It is shown that in partial wave dispersion relations the weight function on the unphysical cut must have a certain number of zeros in order to permit the correct threshold behaviour of the amplitude. Assuming a solution — not necessarily with correct threshold behaviour — of the once-subtractedN/D-equations to exist, the role of the subtraction parameters in repeatedly subtractedN/D equations is studied with particular reference to the threshold behaviour.
Interpretation of KPFM Data with the Weight Function for Charges
2018
The KPFM signal for systems containing local charges can be expressed as a weighted sum over all local charges. The weight function for charges quantifies the contribution of each charge, depending on its position. In this chapter, we evaluate the KPFM weight function for charges by analyzing several application-relevant model systems. The intention of this chapter is to provide insights into the KPFM contrast formation in order to facilitate the KPFM data interpretation. For this, we concentrate on three model systems: (A) a conductive sample in ultra-high vacuum, (B) a dielectric sample in ultra-high vacuum, and (C) a dielectric sample in water. We calculate the weight function for charge…