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A point in the spectrum of a closed linear operator: in the Banach space with domain is said to belong to discrete spectrum of if the following two conditions are satisfied: [1] λ {\displaystyle \lambda } is an isolated point in σ ( A ) {\displaystyle \sigma (A)} ;
Small-angle X-ray scattering (SAXS) is a small-angle scattering technique by which nanoscale density differences in a sample can be quantified. This means that it can determine nanoparticle size distributions, resolve the size and shape of (monodisperse) macromolecules, determine pore sizes and characteristic distances of partially ordered materials. [1]
There exist several efficient designs for analyzing an X-ray emission spectrum in the ultra soft X-ray region. The figure of merit for such instruments is the spectral throughput, i.e. the product of detected intensity and spectral resolving power. Usually, it is possible to change these parameters within a certain range while keeping their ...
The discrete spectrum is defined as the set of normal eigenvalues or, equivalently, as the set of isolated points of the spectrum such that the corresponding Riesz projector is of finite rank. As such, the discrete spectrum is a strict subset of the point spectrum, i.e., σ d ( T ) ⊂ σ p ( T ) . {\displaystyle \sigma _{d}(T)\subset \sigma ...
The continuous and discrete spectra of physical systems can be modeled in functional analysis as different parts in the decomposition of the spectrum of a linear operator acting on a function space, such as the Hamiltonian operator. The classical example of a discrete spectrum (for which the term was first used) is the characteristic set of ...
The analysis of the energy dependence of the emitted photons is the aim of the X-ray emission spectroscopy. [ 1 ] [ 2 ] [ 3 ] XES is also sometimes referred to as X-ray Fluorescence (XRF) spectroscopy, and while the terms can be used interchangeably, XES more often describes high energy resolution techniques [ 4 ] while XRF studies a wider ...
The spectrum of T is the set of all complex numbers ζ such that R ζ fails to exist or is unbounded. Often the spectrum of T is denoted by σ(T). The function R ζ for all ζ in ρ(T) (that is, wherever R ζ exists as a bounded operator) is called the resolvent of T. The spectrum of T is therefore the complement of the resolvent set of T in ...
Particle-Induced X-Ray Emission or Proton-Induced X-Ray Emission (PIXE) is a technique used for determining the elemental composition of a material or a sample. When a material is exposed to an ion beam, atomic interactions occur that give off EM radiation of wavelengths in the x-ray part of the electromagnetic spectrum specific to an element.