Gauss–Markov theoremIn statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. The errors do not need to be normal, nor do they need to be independent and identically distributed (only uncorrelated with mean zero and homoscedastic with finite variance).
Distance correlationIn statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.
N-Butyllithiumn-Butyllithium C4H9Li (abbreviated n-BuLi) is an organolithium reagent. It is widely used as a polymerization initiator in the production of elastomers such as polybutadiene or styrene-butadiene-styrene (SBS). Also, it is broadly employed as a strong base (superbase) in the synthesis of organic compounds as in the pharmaceutical industry. Butyllithium is commercially available as solutions (15%, 25%, 1.5 M, 2 M, 2.5 M, 10 M, etc.) in alkanes such as pentane, hexanes, and heptanes.
Base (chemistry)In chemistry, there are three definitions in common use of the word "base": Arrhenius bases, Brønsted bases, and Lewis bases. All definitions agree that bases are substances that react with acids, as originally proposed by G.-F. Rouelle in the mid-18th century. In 1884, Svante Arrhenius proposed that a base is a substance which dissociates in aqueous solution to form hydroxide ions OH−. These ions can react with hydrogen ions (H+ according to Arrhenius) from the dissociation of acids to form water in an acid–base reaction.
Factor analysisFactor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables.
HydroniumIn chemistry, hydronium (hydroxonium in traditional British English) is the common name for the aqueous cation , the type of oxonium ion produced by protonation of water. It is often viewed as the positive ion present when an Arrhenius acid is dissolved in water, as Arrhenius acid molecules in solution give up a proton (a positive hydrogen ion, ) to the surrounding water molecules (). In fact, acids must be surrounded by more than a single water molecule in order to ionize, yielding aqueous and conjugate base.
Extent of reactionIn physical chemistry and chemical engineering, extent of reaction is a quantity that measures the extent to which the reaction has proceeded. Often, it refers specifically to the value of the extent of reaction when equilibrium has been reached. It is usually denoted by the Greek letter ξ. The extent of reaction is usually defined so that it has units of amount (moles). It was introduced by the Belgian scientist Théophile de Donder. Consider the reaction A ⇌ 2 B + 3 C Suppose an infinitesimal amount of the reactant A changes into B and C.
IsopentaneIsopentane, also called methylbutane or 2-methylbutane, is a branched-chain saturated hydrocarbon (an alkane) with five carbon atoms, with formula C5H12 or CH(CH3)2(C2H5). Isopentane is a volatile and flammable liquid. It is one of three structural isomers with the molecular formula C5H12, the others being pentane (n-pentane) and neopentane (dimethyl propane). Isopentane is commonly used in conjunction with liquid nitrogen to achieve a liquid bath temperature of −160 °C.
GasGas is one of the four fundamental states of matter. The others are solid, liquid, and plasma. A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles.
Linear discriminant analysisLinear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
