Multivariate normal distributionIn probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
Transition metalIn chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be transition metals as well. Since they are metals, they are lustrous and have good electrical and thermal conductivity.
Electric dipole momentThe electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry. Theoretically, an electric dipole is defined by the first-order term of the multipole expansion; it consists of two equal and opposite charges that are infinitesimally close together, although real dipoles have separated charge.
Complex normal distributionIn probability theory, the family of complex normal distributions, denoted or , characterizes complex random variables whose real and imaginary parts are jointly normal. The complex normal family has three parameters: location parameter μ, covariance matrix , and the relation matrix . The standard complex normal is the univariate distribution with , , and . An important subclass of complex normal family is called the circularly-symmetric (central) complex normal and corresponds to the case of zero relation matrix and zero mean: and .
PolystyrenePolystyrene (PS) ˌpɒliˈstaɪriːn is a synthetic polymer made from monomers of the aromatic hydrocarbon styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and brittle. It is an inexpensive resin per unit weight. It is a poor barrier to oxygen and water vapor and has a relatively low melting point. Polystyrene is one of the most widely used plastics, with the scale of its production being several million tonnes per year. Polystyrene is naturally transparent, but can be colored with colorants.
Magnetic momentIn electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets), permanent magnets, elementary particles (such as electrons), composite particles (such as protons and neutrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc).
PolymerizationIn polymer chemistry, polymerization (American English), or polymerisation (British English), is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks. There are many forms of polymerization and different systems exist to categorize them. In chemical compounds, polymerization can occur via a variety of reaction mechanisms that vary in complexity due to the functional groups present in the reactants and their inherent steric effects.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
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.
Rotational–vibrational spectroscopyRotational–vibrational spectroscopy is a branch of molecular spectroscopy concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational (or ro-vibrational) transitions. When such transitions emit or absorb photons (electromagnetic radiation), the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy.
Organic photochemistryOrganic photochemistry encompasses organic reactions that are induced by the action of light. The absorption of ultraviolet light by organic molecules often leads to reactions. In the earliest days, sunlight was employed, while in more modern times ultraviolet lamps are employed. Organic photochemistry has proven to be a very useful synthetic tool. Complex organic products can be obtained simply. Early examples were often uncovered by the observation of precipitates or color changes from samples that were exposed to sunlights.
EthyleneEthylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon–carbon double bonds). Ethylene is widely used in the chemical industry, and its worldwide production (over 150 million tonnes in 2016) exceeds that of any other organic compound. Much of this production goes toward polyethylene, a widely used plastic containing polymer chains of ethylene units in various chain lengths.
