Infrared spectroscopyInfrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer (or spectrophotometer) which produces an infrared spectrum.
Point groupIn geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d). Point groups are used to describe the symmetries of geometric figures and physical objects such as molecules. Each point group can be represented as sets of orthogonal matrices M that transform point x into point y according to y = Mx.
Near-infrared spectroscopyNear-infrared spectroscopy (NIRS) is a spectroscopic method that uses the near-infrared region of the electromagnetic spectrum (from 780 nm to 2500 nm). Typical applications include medical and physiological diagnostics and research including blood sugar, pulse oximetry, functional neuroimaging, sports medicine, elite sports training, ergonomics, rehabilitation, neonatal research, brain computer interface, urology (bladder contraction), and neurology (neurovascular coupling).
InfraredInfrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than those of visible light and shorter than radio waves. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around 1 millimeter (300 GHz) to the nominal red edge of the visible spectrum, around 700 nanometers (430 THz). IR is commonly divided between longer-wavelength thermal infrared that is emitted from terrestrial sources and shorter-wavelength near-infrared that is part of the solar spectrum.
Fourier-transform infrared spectroscopyFourier-transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas. An FTIR spectrometer simultaneously collects high-resolution spectral data over a wide spectral range. This confers a significant advantage over a dispersive spectrometer, which measures intensity over a narrow range of wavelengths at a time. The term Fourier-transform infrared spectroscopy originates from the fact that a Fourier transform (a mathematical process) is required to convert the raw data into the actual spectrum.
Open sourceOpen source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized software development model that encourages open collaboration. A main principle of open-source software development is peer production, with products such as source code, blueprints, and documentation freely available to the public.
Point reflectionIn geometry, a point reflection (also called a point inversion or central inversion) is an transformation of affine space in which every point is reflected across a specific fixed point. A point reflection is an involution: applying it twice is the identity transformation. It is equivalent to a homothetic transformation with scale factor −1. The point of inversion is also called homothetic center. An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Point groups in three dimensionsIn geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetries.
Point groups in four dimensionsIn geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere. 1889 Édouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales Scientifiques de l'École Normale Supérieure, Sér. 3, 6, (pp. 9–102, pp. 80–81 tetrahedra), Goursat tetrahedron 1951, A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Proceedings of the Cambridge Philosophical Society, vol.
Point groups in two dimensionsIn geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group.
Crystallographic point groupIn crystallography, a crystallographic point group is a set of symmetry operations, corresponding to one of the point groups in three dimensions, such that each operation (perhaps followed by a translation) would leave the structure of a crystal unchanged i.e. the same kinds of atoms would be placed in similar positions as before the transformation.
RebreatherA rebreather is a breathing apparatus that absorbs the carbon dioxide of a user's exhaled breath to permit the rebreathing (recycling) of the substantially unused oxygen content, and unused inert content when present, of each breath. Oxygen is added to replenish the amount metabolised by the user. This differs from open-circuit breathing apparatus, where the exhaled gas is discharged directly into the environment.
Log-normal distributionIn probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
Group theoryIn abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
One-dimensional symmetry groupA one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x).
Mode (statistics)The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e, x=argmaxxi P(X = xi)). In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.
Independent and identically distributed random variablesIn probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as i.i.d., iid, or IID. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Statistics commonly deals with random samples. A random sample can be thought of as a set of objects that are chosen randomly.
Open-source software developmentOpen-source software development (OSSD) is the process by which open-source software, or similar software whose source code is publicly available, is developed by an open-source software project. These are software products available with its source code under an open-source license to study, change, and improve its design. Examples of some popular open-source software products are Mozilla Firefox, Google Chromium, Android, LibreOffice and the VLC media player. In 1997, Eric S. Raymond wrote The Cathedral and the Bazaar.
Open-source hardwareOpen-source hardware (OSH) consists of physical artifacts of technology designed and offered by the open-design movement. Both free and open-source software (FOSS) and open-source hardware are created by this open-source culture movement and apply a like concept to a variety of components. It is sometimes, thus, referred to as FOSH (free and open-source hardware). The term usually means that information about the hardware is easily discerned so that others can make it – coupling it closely to the maker movement.
