Multinomial logistic regressionIn statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).
Content analysisContent analysis is the study of documents and communication artifacts, which might be texts of various formats, pictures, audio or video. Social scientists use content analysis to examine patterns in communication in a replicable and systematic manner. One of the key advantages of using content analysis to analyse social phenomena is their non-invasive nature, in contrast to simulating social experiences or collecting survey answers. Practices and philosophies of content analysis vary between academic disciplines.
GeneIn biology, the word gene (from γένος, génos; meaning generation or birth or gender) can have several different meanings. The Mendelian gene is a basic unit of heredity and the molecular gene is a sequence of nucleotides in DNA that is transcribed to produce a functional RNA. There are two types of molecular genes: protein-coding genes and noncoding genes. During gene expression, the DNA is first copied into RNA. The RNA can be directly functional or be the intermediate template for a protein that performs a function.
Lefschetz fixed-point theoremIn mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space to itself by means of traces of the induced mappings on the homology groups of . It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle).
Brouwer fixed-point theoremBrouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function mapping a nonempty compact convex set to itself there is a point such that . The simplest forms of Brouwer's theorem are for continuous functions from a closed interval in the real numbers to itself or from a closed disk to itself. A more general form than the latter is for continuous functions from a nonempty convex compact subset of Euclidean space to itself.
Traité de mécanique célesteTraité de mécanique céleste () is a five-volume treatise on celestial mechanics written by Pierre-Simon Laplace and published from 1798 to 1825 with a second edition in 1829. In 1842, the government of Louis Philippe gave a grant of 40,000 francs for a 7-volume national edition of the Oeuvres de Laplace (1843–1847); the Traité de mécanique céleste with its four supplements occupies the first 5 volumes. Newton laid the foundations of Celestial Mechanics, at the close of the seventeenth century, by the discovery of the principle of universal gravitation.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Model aircraftA model aircraft is a small unmanned aircraft. Many are replicas of real aircraft. Model aircraft are divided into two basic groups: flying and non-flying. Non-flying models are also termed static, display, or shelf models. Aircraft manufacturers and researchers make wind tunnel models for testing aerodynamic properties, for basic research, or for the development of new designs. Sometimes only part of the aircraft is modelled.
ConcentrationIn chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes and solvents in solutions. The molar (amount) concentration has variants, such as normal concentration and osmotic concentration. Dilution is reduction of concentration, e.
Molar concentrationMolar concentration (also called molarity, amount concentration or substance concentration) is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm3 in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.
Nuclear magnetic resonance spectra databaseA nuclear magnetic resonance spectra database is an electronic repository of information concerning Nuclear magnetic resonance (NMR) spectra. Such repositories can be downloaded as self-contained data sets or used online. The form in which the data is stored varies, ranging from line lists that can be graphically displayed to raw free induction decay (FID) data. Data is usually annotated in a way that correlates the spectral data with the related molecular structure. The form in which most NMR is described in literature papers.
Definite quadratic formIn mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the same way, except that "always positive" and "always negative" are replaced by "never negative" and "never positive", respectively.
