NanoparticleA nanoparticle or ultrafine particle is usually defined as a particle of matter that is between 1 and 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At the lowest range, metal particles smaller than 1 nm are usually called atom clusters instead.
Colloidal goldColloidal gold is a sol or colloidal suspension of nanoparticles of gold in a fluid, usually water. The colloid is coloured usually either wine red (for spherical particles less than 100 nm) or blue-purple (for larger spherical particles or nanorods). Due to their optical, electronic, and molecular-recognition properties, gold nanoparticles are the subject of substantial research, with many potential or promised applications in a wide variety of areas, including electron microscopy, electronics, nanotechnology, materials science, and biomedicine.
Integral transformIn mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the inverse transform. An integral transform is any transform of the following form: The input of this transform is a function , and the output is another function .
Raman spectroscopyRaman spectroscopy (ˈrɑːmən) (named after Indian physicist C. V. Raman) is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified. Raman spectroscopy relies upon inelastic scattering of photons, known as Raman scattering.
Fourier transformIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
Silver nanoparticleSilver nanoparticles are nanoparticles of silver of between 1 nm and 100 nm in size. While frequently described as being 'silver' some are composed of a large percentage of silver oxide due to their large ratio of surface to bulk silver atoms. Numerous shapes of nanoparticles can be constructed depending on the application at hand. Commonly used silver nanoparticles are spherical, but diamond, octagonal, and thin sheets are also common. Their extremely large surface area permits the coordination of a vast number of ligands.
Hilbert transformIn mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces another function of a real variable H(u)(t). The Hilbert transform is given by the Cauchy principal value of the convolution with the function (see ). The Hilbert transform has a particularly simple representation in the frequency domain: It imparts a phase shift of ±90° ( radians) to every frequency component of a function, the sign of the shift depending on the sign of the frequency (see ).
Resonance Raman spectroscopyResonance Raman spectroscopy (RR spectroscopy or RRS) is a variant of Raman spectroscopy in which the incident photon energy is close in energy to an electronic transition of a compound or material under examination. This similarity in energy (resonance) leads to greatly increased intensity of the Raman scattering of certain vibrational modes, compared to ordinary Raman spectroscopy. Resonance Raman spectroscopy has much greater sensitivity than non-resonance Raman spectroscopy, allowing for the analysis of compounds with inherently weak Raman scattering intensities, or at very low concentrations.
Discrete Fourier transformIn mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.
Multidimensional transformIn mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation. The discrete-domain multidimensional Fourier transform (FT) can be computed as follows: where F stands for the multidimensional Fourier transform, m stands for multidimensional dimension.
