QR decompositionIn linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Any real square matrix A may be decomposed as where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning ) and R is an upper triangular matrix (also called right triangular matrix).
CementA cement is a binder, a chemical substance used for construction that sets, hardens, and adheres to other materials to bind them together. Cement is seldom used on its own, but rather to bind sand and gravel (aggregate) together. Cement mixed with fine aggregate produces mortar for masonry, or with sand and gravel, produces concrete. Concrete is the most widely used material in existence and is behind only water as the planet's most-consumed resource.
Cement clinkerCement clinker is a solid material produced in the manufacture of Portland cement as an intermediary product. Clinker occurs as lumps or nodules, usually to in diameter. It is produced by sintering (fusing together without melting to the point of liquefaction) limestone and aluminosilicate materials such as clay during the cement kiln stage. The Portland clinker essentially consists of four minerals: two calcium silicates, alite (Ca3SiO5) and belite (Ca2SiO4), along with tricalcium aluminate (Ca3Al2O6) and calcium aluminoferrite (Ca2(Al,Fe)2O5).
LU decompositionIn numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix.
Portland cementPortland cement is the most common type of cement in general use around the world as a basic ingredient of concrete, mortar, stucco, and non-specialty grout. It was developed from other types of hydraulic lime in England in the early 19th century by Joseph Aspdin, and is usually made from limestone. It is a fine powder, produced by heating limestone and clay minerals in a kiln to form clinker, grinding the clinker, and adding 2 to 3 percent of gypsum. Several types of portland cement are available.
Energetically modified cementEnergetically modified cements (EMCs) are a class of cements made from pozzolans (e.g. fly ash, volcanic ash, pozzolana), silica sand, blast furnace slag, or Portland cement (or blends of these ingredients). The term "energetically modified" arises by virtue of the mechanochemistry process applied to the raw material, more accurately classified as "high energy ball milling" (HEBM). This causes, amongst others, a thermodynamic transformation in the material to increase its chemical reactivity.
DecompositionDecomposition or rot is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and is essential for recycling the finite matter that occupies physical space in the biosphere. Bodies of living organisms begin to decompose shortly after death. Animals, such as worms, also help decompose the organic materials. Organisms that do this are known as decomposers or detritivores.
Mortar (masonry)Mortar is a workable paste which hardens to bind building blocks such as stones, bricks, and concrete masonry units, to fill and seal the irregular gaps between them, spread the weight of them evenly, and sometimes to add decorative colors or patterns to masonry walls. In its broadest sense, mortar includes pitch, asphalt, and soft mud or clay, as those used between mud bricks, as well as cement mortar. The word "mortar" comes from Old French mortier, "builder's mortar, plaster; bowl for mixing." (13c.).
Cholesky decompositionIn linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ʃəˈlɛski ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations.
Polar decompositionIn mathematics, the polar decomposition of a square real or complex matrix is a factorization of the form , where is a unitary matrix and is a positive semi-definite Hermitian matrix ( is an orthogonal matrix and is a positive semi-definite symmetric matrix in the real case), both square and of the same size. Intuitively, if a real matrix is interpreted as a linear transformation of -dimensional space , the polar decomposition separates it into a rotation or reflection of , and a scaling of the space along a set of orthogonal axes.
Mortar (weapon)A mortar is usually a simple, lightweight, man-portable, muzzle-loaded weapon, consisting of a smooth-bore (although some models use a rifled barrel) metal tube fixed to a base plate (to spread out the recoil) with a lightweight bipod mount and a sight. They launch explosive shells (technically called bombs) in high-arcing ballistic trajectories. Mortars are typically used as indirect fire weapons for close fire support with a variety of ammunition. Mortars have been used for hundreds of years.
Stokes mortarThe Stokes mortar was a British trench mortar designed by Sir Wilfred Stokes KBE that was issued to the British and U.S. armies, as well as the Portuguese Expeditionary Corps, during the latter half of the First World War. The 3-inch trench mortar is a smooth-bore, muzzle-loading weapon for high angles of fire. Although it is called a 3-inch mortar, its bore is actually 3.2 inches or 81 mm. The Stokes mortar was a simple weapon, consisting of a smoothbore metal tube fixed to a base plate (to absorb recoil) with a lightweight bipod mount.
Compressive strengthIn mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.
Singular value decompositionIn linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an complex matrix M is a factorization of the form where U is an complex unitary matrix, is an rectangular diagonal matrix with non-negative real numbers on the diagonal, V is an complex unitary matrix, and is the conjugate transpose of V.
Ultimate tensile strengthUltimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher. The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain.
Strength of materialsThe field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.
Dental cementDental cements have a wide range of dental and orthodontic applications. Common uses include temporary restoration of teeth, cavity linings to provide pulpal protection, sedation or insulation and cementing fixed prosthodontic appliances. Recent uses of dental cement also include two-photon calcium imaging of neuronal activity in brains of animal models in basic experimental neuroscience. Traditionally cements have separate powder and liquid components which are manually mixed.
ConcreteConcrete is a composite material composed of aggregate bonded together with a fluid cement that cures over time. Concrete is the second-most-used substance in the world after water, and is the most widely used building material. Its usage worldwide, ton for ton, is twice that of steel, wood, plastics, and aluminium combined. When aggregate is mixed with dry Portland cement and water, the mixture forms a fluid slurry that is easily poured and molded into shape.
PlasterworkPlasterwork is construction or ornamentation done with plaster, such as a layer of plaster on an interior or exterior wall structure, or plaster decorative moldings on ceilings or walls. This is also sometimes called pargeting. The process of creating plasterwork, called plastering or rendering, has been used in building construction for centuries. For the art history of three-dimensional plaster, see stucco. The earliest plasters known to us were lime-based.
Lime (material)Lime is an inorganic material composed primarily of calcium oxides and hydroxides, usually calcium oxide and/or calcium hydroxide. It is also the name for calcium oxide which occurs as a product of coal-seam fires and in altered limestone xenoliths in volcanic ejecta. The International Mineralogical Association recognizes lime as a mineral with the chemical formula of CaO. The word lime originates with its earliest use as building mortar and has the sense of sticking or adhering.
