DimensionIn physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.
Cadmium sulfideCadmium sulfide is the inorganic compound with the formula CdS. Cadmium sulfide is a yellow solid. It occurs in nature with two different crystal structures as the rare minerals greenockite and hawleyite, but is more prevalent as an impurity substituent in the similarly structured zinc ores sphalerite and wurtzite, which are the major economic sources of cadmium. As a compound that is easy to isolate and purify, it is the principal source of cadmium for all commercial applications.
One-dimensional spaceIn physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number. In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself.
Space groupIn mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219 distinct types, or 230 types if chiral copies are considered distinct. Space groups are discrete cocompact groups of isometries of an oriented Euclidean space in any number of dimensions.
Four-dimensional spaceFour-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).
Three-dimensional spaceIn geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.
New neoclassical synthesisThe new neoclassical synthesis (NNS), which is now generally referred to as New Keynesian economics, and occasionally as the New Consensus, is the fusion of the major, modern macroeconomic schools of thought – new classical macroeconomics/real business cycle theory and early New Keynesian economics – into a consensus view on the best way to explain short-run fluctuations in the economy. This new synthesis is analogous to the neoclassical synthesis that combined neoclassical economics with Keynesian macroeconomics.
Neoclassical synthesisThe neoclassical synthesis (NCS), neoclassical–Keynesian synthesis, or just neo-Keynesianism was a neoclassical economics academic movement and paradigm in economics that worked towards reconciling the macroeconomic thought of John Maynard Keynes in his book The General Theory of Employment, Interest and Money (1936). It was formulated most notably by John Hicks (1937), Franco Modigliani (1944), and Paul Samuelson (1948), who dominated economics in the post-war period and formed the mainstream of macroeconomic thought in the 1950s, 60s, and 70s.
Coordination complexA coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those that include transition metals (elements like titanium that belong to the periodic table's d-block), are coordination complexes. Coordination complexes are so pervasive that their structures and reactions are described in many ways, sometimes confusingly.
CadmiumCadmium is a chemical element with the symbol Cd and atomic number 48. This soft, silvery-white metal is chemically similar to the two other stable metals in group 12, zinc and mercury. Like zinc, it demonstrates oxidation state +2 in most of its compounds, and like mercury, it has a lower melting point than the transition metals in groups 3 through 11. Cadmium and its congeners in group 12 are often not considered transition metals, in that they do not have partly filled d or f electron shells in the elemental or common oxidation states.
Covalent bondA covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding.
New classical macroeconomicsNew classical macroeconomics, sometimes simply called new classical economics, is a school of thought in macroeconomics that builds its analysis entirely on a neoclassical framework. Specifically, it emphasizes the importance of rigorous foundations based on microeconomics, especially rational expectations. New classical macroeconomics strives to provide neoclassical microeconomic foundations for macroeconomic analysis.
Potassium ferricyanidePotassium ferricyanide is the chemical compound with the formula K3[Fe(CN)6]. This bright red salt contains the octahedrally coordinated [Fe(CN)6]3− ion. It is soluble in water and its solution shows some green-yellow fluorescence. It was discovered in 1822 by Leopold Gmelin. Potassium ferricyanide is manufactured by passing chlorine through a solution of potassium ferrocyanide. Potassium ferricyanide separates from the solution: 2 K4[Fe(CN)6] + Cl2 → 2 K3[Fe(CN)6] + 2 KCl Like other metal cyanides, solid potassium ferricyanide has a complicated polymeric structure.
Water of crystallizationIn chemistry, water(s) of crystallization or water(s) of hydration are water molecules that are present inside crystals. Water is often incorporated in the formation of crystals from aqueous solutions. In some contexts, water of crystallization is the total mass of water in a substance at a given temperature and is mostly present in a definite (stoichiometric) ratio. Classically, "water of crystallization" refers to water that is found in the crystalline framework of a metal complex or a salt, which is not directly bonded to the metal cation.
AtomAn atom is a particle that consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. The atom is the basic particle of the chemical elements, and the chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. The number of neutrons defines the isotope of the element. Atoms are extremely small, typically around 100 picometers across.
Beta decayIn nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission.
Dimensional analysisIn engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.
CarboxylateIn organic chemistry, a carboxylate is the conjugate base of a carboxylic acid, (or ). It is an ion with negative charge. Carboxylate salts are salts that have the general formula , where M is a metal and n is 1, 2,.... Carboxylate esters have the general formula (also written as ), where R and R′ are organic groups. Carboxylate ions can be formed by deprotonation of carboxylic acids. Such acids typically have pKa of less than 5, meaning that they can be deprotonated by many bases, such as sodium hydroxide or sodium bicarbonate.
Beta particleA beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β− decay and β+ decay, which produce electrons and positrons respectively. Beta particles with an energy of 0.5 MeV have a range of about one metre in the air; the distance is dependent on the particle energy.
Lewis acids and basesA Lewis acid (named for the American physical chemist Gilbert N. Lewis) is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any species that has a filled orbital containing an electron pair which is not involved in bonding but may form a dative bond with a Lewis acid to form a Lewis adduct. For example, NH3 is a Lewis base, because it can donate its lone pair of electrons.
