Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
FormulationFormulation is a term used in various senses in various applications, both the material and the abstract or formal. Its fundamental meaning is the putting together of components in appropriate relationships or structures, according to a formula. Etymologically formula is the diminutive of the Latin forma, meaning shape. In that sense a formulation is created according to the standard for the product. Disciplines in which one might use the word formulation in the abstract sense include logic, mathematics, linguistics, legal theory, and computer science.
Matrix multiplicationIn mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Cross-linked polyethyleneCross-linked polyethylene, commonly abbreviated PEX, XPE or XLPE, is a form of polyethylene with cross-links. It is used predominantly in building services pipework systems, hydronic radiant heating and cooling systems, domestic water piping, insulation for high tension (high voltage) electrical cables, and baby play mats. It is also used for natural gas and offshore oil applications, chemical transportation, and transportation of sewage and slurries.
PolyethylenePolyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most commonly produced plastic. It is a polymer, primarily used for packaging (plastic bags, plastic films, geomembranes and containers including bottles, etc.). , over 100 million tonnes of polyethylene resins are being produced annually, accounting for 34% of the total plastics market. Many kinds of polyethylene are known, with most having the chemical formula (C2H4)n. PE is usually a mixture of similar polymers of ethylene, with various values of n.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Hausdorff dimensionIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension.
Benoit MandelbrotBenoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.
Electron microscopeAn electron microscope is a microscope that uses a beam of electrons as a source of illumination. They use electron optics that are analogous to the glass lenses of an optical light microscope. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light, electron microscopes have a higher resolution of about 0.1 nm, which compares to about 200 nm for light microscopes.
Curing (chemistry)Curing is a chemical process employed in polymer chemistry and process engineering that produces the toughening or hardening of a polymer material by cross-linking of polymer chains. Even if it is strongly associated with the production of thermosetting polymers, the term "curing" can be used for all the processes where a solid product is obtained from a liquid solution, such as with PVC plastisols. During the curing process, single monomers and oligomers, mixed with or without a curing agent, react to form a tridimensional polymeric network.
