QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
Astronomical spectroscopyAstronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars and other celestial objects. A stellar spectrum can reveal many properties of stars, such as their chemical composition, temperature, density, mass, distance and luminosity. Spectroscopy can show the velocity of motion towards or away from the observer by measuring the Doppler shift.
MassMass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent.
DiboraneDiborane(6), commonly known as diborane, is the chemical compound with the formula B2H6. It is a toxic, colorless, and pyrophoric gas with a repulsively sweet odor. Given its simple formula, borane is a fundamental boron compound. It has attracted wide attention for its electronic structure. Several of its derivatives are useful reagents. The structure of diborane has D2h symmetry. Four hydrides are terminal, while two bridge between the boron centers. The lengths of the B–Hbridge bonds and the B–Hterminal bonds are 1.
Gaseous diffusionGaseous diffusion is a technology that was used to produce enriched uranium by forcing gaseous uranium hexafluoride (UF6) through microporous membranes. This produces a slight separation (enrichment factor 1.0043) between the molecules containing uranium-235 (235U) and uranium-238 (238U). By use of a large cascade of many stages, high separations can be achieved. It was the first process to be developed that was capable of producing enriched uranium in industrially useful quantities, but is nowadays considered obsolete, having been superseded by the more-efficient gas centrifuge process.
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Chemical polarityIn chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. Polar molecules must contain one or more polar bonds due to a difference in electronegativity between the bonded atoms. Molecules containing polar bonds have no molecular polarity if the bond dipoles cancel each other out by symmetry. Polar molecules interact through dipole-dipole intermolecular forces and hydrogen bonds.
Molecular cloudA molecular cloud, sometimes called a stellar nursery (if star formation is occurring within), is a type of interstellar cloud, the density and size of which permit absorption nebulae, the formation of molecules (most commonly molecular hydrogen, H2), and the formation of H II regions. This is in contrast to other areas of the interstellar medium that contain predominantly ionized gas. Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is carbon monoxide (CO).
Polar decompositionIn mathematics, the polar decomposition of a square real or complex matrix is a factorization of the form , where is a unitary matrix and is a positive semi-definite Hermitian matrix ( is an orthogonal matrix and is a positive semi-definite symmetric matrix in the real case), both square and of the same size. Intuitively, if a real matrix is interpreted as a linear transformation of -dimensional space , the polar decomposition separates it into a rotation or reflection of , and a scaling of the space along a set of orthogonal axes.
Physical objectIn common usage and classical mechanics, a physical object or physical body (or simply an object or body) is a collection of matter within a defined contiguous boundary in three-dimensional space. The boundary surface must be defined and identified by the properties of the material, although it may change over time. The boundary is usually the visible or tangible surface of the object. The matter in the object is constrained (to a greater or lesser degree) to move as one object.
Differential thermal analysisDifferential thermal analysis (DTA) is a thermoanalytic technique that is similar to differential scanning calorimetry. In DTA, the material under study and an inert reference are made to undergo identical thermal cycles, (i.e., same cooling or heating programme) while recording any temperature difference between sample and reference. This differential temperature is then plotted against time, or against temperature (DTA curve, or thermogram). Changes in the sample, either exothermic or endothermic, can be detected relative to the inert reference.
Chemical ionizationChemical ionization (CI) is a soft ionization technique used in mass spectrometry. This was first introduced by Burnaby Munson and Frank H. Field in 1966. This technique is a branch of gaseous ion-molecule chemistry. Reagent gas molecules (often methane or ammonia) are ionized by electron ionization to form reagent ions, which subsequently react with analyte molecules in the gas phase to create analyte ions for analysis by mass spectrometry.
