Separable extensionIn field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more general definition that applies when E is not necessarily algebraic over F. An extension that is not separable is said to be inseparable.
Group extensionIn mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If and are two groups, then is an extension of by if there is a short exact sequence If is an extension of by , then is a group, is a normal subgroup of and the quotient group is isomorphic to the group . Group extensions arise in the context of the extension problem, where the groups and are known and the properties of are to be determined.
Linear elasticityLinear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.
Solid mechanicsSolid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents. Solid mechanics is fundamental for civil, aerospace, nuclear, biomedical and mechanical engineering, for geology, and for many branches of physics and chemistry such as materials science.
QuantityQuantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties. Quantity is among the basic classes of things along with quality, substance, change, and relation.
Deformation (engineering)In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve.
Spring (device)A spring is a device consisting of an elastic but largely rigid material (typically metal) bent or molded into a form (especially a coil) that can return into shape after being compressed or extended. Springs can store energy when compressed. In everyday use the term often refers to coil springs, but there are many different spring designs. Modern springs are typically manufactured from spring steel. An example of a non-metallic spring is the bow, made traditionally of flexible yew wood, which when drawn stores energy to propel an arrow.
PistonA piston is a component of reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from expanding gas in the cylinder to the crankshaft via a piston rod and/or connecting rod. In a pump, the function is reversed and force is transferred from the crankshaft to the piston for the purpose of compressing or ejecting the fluid in the cylinder.
Position (geometry)In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P: The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.
Normal extensionIn abstract algebra, a normal extension is an algebraic field extension L/K for which every irreducible polynomial over K which has a root in L, splits into linear factors in L. These are one of the conditions for algebraic extensions to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. Let be an algebraic extension (i.e. L is an algebraic extension of K), such that (i.e. L is contained in an algebraic closure of K).
