One-dimensional symmetry groupA one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x. The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, A1, [ ], or Coxeter-Dynkin diagram . Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x).
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.
BerylliumBeryllium is a chemical element with the symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form minerals. Gemstones high in beryllium include beryl (aquamarine, emerald, red beryl) and chrysoberyl. It is a relatively rare element in the universe, usually occurring as a product of the spallation of larger atomic nuclei that have collided with cosmic rays.
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.
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.
Atomic emission spectroscopyAtomic emission spectroscopy (AES) is a method of chemical analysis that uses the intensity of light emitted from a flame, plasma, arc, or spark at a particular wavelength to determine the quantity of an element in a sample. The wavelength of the atomic spectral line in the emission spectrum gives the identity of the element while the intensity of the emitted light is proportional to the number of atoms of the element. The sample may be excited by various methods.
Dimension (vector space)In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say is if the dimension of is finite, and if its dimension is infinite.
Crystal systemIn crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family. The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic.
Crystal twinningCrystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane. Crystallographers classify twinned crystals by a number of twin laws. These twin laws are specific to the crystal structure.
Prussian bluePrussian blue also known as Berlin blue, Brandenburg blue, Parisian and Paris blue is a dark blue pigment produced by oxidation of ferrous ferrocyanide salts. It has the chemical formula Fe[Fe(CN)]. Turnbull's blue is chemically identical, but is made from different reagents, and its slightly different color stems from different impurities and particle sizes. Prussian blue was created in the early 18th century and is the first modern synthetic pigment. It is prepared as a very fine colloidal dispersion, because the compound is not soluble in water.
Zero-dimensional spaceIn mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. A graphical illustration of a nildimensional space is a point. Specifically: A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every open cover of the space has a refinement which is a cover by disjoint open sets.
PyrolysisThe pyrolysis (or devolatilization) process is the thermal decomposition of materials at elevated temperatures, often in an inert atmosphere. Temperature can be understood as thermal vibration. At high temperatures, excessive vibration causes long chain molecules to break into smaller molecules. The word is coined from the Greek-derived elements pyro "fire", "heat", "fever" and lysis "separating". Pyrolysis is most commonly used in the treatment of organic materials. It is one of the processes involved in charring wood.
