Maxwell's equationsMaxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.
EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Inertial navigation systemAn inertial navigation system (INS) is a navigation device that uses motion sensors (accelerometers), rotation sensors (gyroscopes) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity (direction and speed of movement) of a moving object without the need for external references. Often the inertial sensors are supplemented by a barometric altimeter and sometimes by magnetic sensors (magnetometers) and/or speed measuring devices.
Quadratic equationIn algebra, a quadratic equation () is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.
Einstein field equationsIn the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Albert Einstein in 1915 in the form of a tensor equation which related the local (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor).
Inertial frame of referenceIn classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds.
Equations of motionIn physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
Rotation matrixIn linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: If x and y are the endpoint coordinates of a vector, where x is cosine and y is sine, then the above equations become the trigonometric summation angle formulae.
Moving frameIn mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry of smooth manifolds embedded in a homogeneous space. In lay terms, a frame of reference is a system of measuring rods used by an observer to measure the surrounding space by providing coordinates. A moving frame is then a frame of reference which moves with the observer along a trajectory (a curve).
Polar coordinate systemIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth.
Dependent and independent variablesDependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.
Errors-in-variables modelsIn statistics, errors-in-variables models or measurement error models are regression models that account for measurement errors in the independent variables. In contrast, standard regression models assume that those regressors have been measured exactly, or observed without error; as such, those models account only for errors in the dependent variables, or responses. In the case when some regressors have been measured with errors, estimation based on the standard assumption leads to inconsistent estimates, meaning that the parameter estimates do not tend to the true values even in very large samples.
France in the Middle AgesThe Kingdom of France in the Middle Ages (roughly, from the 10th century to the middle of the 15th century) was marked by the fragmentation of the Carolingian Empire and West Francia (843–987); the expansion of royal control by the House of Capet (987–1328), including their struggles with the virtually independent principalities (duchies and counties, such as the Norman and Angevin regions), and the creation and extension of administrative/state control (notably under Philip II Augustus and Louis IX) in the
Lorentz transformationIn physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.
Imperative moodThe imperative mood is a grammatical mood that forms a command or request. The imperative mood is used to demand or require that an action be performed. It is usually found only in the present tense, second person. They are sometimes called directives, as they include a feature that encodes directive force, and another feature that encodes modality of unrealized interpretation. An example of a verb used in the imperative mood is the English phrase "Go.
Encephalization quotientEncephalization quotient (EQ), encephalization level (EL), or just encephalization is a relative brain size measure that is defined as the ratio between observed and predicted brain mass for an animal of a given size, based on nonlinear regression on a range of reference species. It has been used as a proxy for intelligence and thus as a possible way of comparing the intelligence levels of different species. For this purpose, it is a more refined measurement than the raw brain-to-body mass ratio, as it takes into account allometric effects.
Equalization (audio)Equalization, or simply EQ, in sound recording and reproduction is the process of adjusting the volume of different frequency bands within an audio signal. The circuit or equipment used to achieve this is called an equalizer. Most hi-fi equipment uses relatively simple filters to make bass and treble adjustments. Graphic and parametric equalizers have much more flexibility in tailoring the frequency content of an audio signal.
InflectionIn linguistic morphology, inflection (or inflexion) is a process of word formation in which a word is modified to express different such as tense, case, voice, aspect, person, number, gender, mood, animacy, and definiteness. The inflection of verbs is called conjugation, and one can refer to the inflection of nouns, adjectives, adverbs, pronouns, determiners, participles, prepositions and postpositions, numerals, articles, etc., as declension.
Haplogroup R1aHaplogroup R1a, or haplogroup R-M420, is a human Y-chromosome DNA haplogroup which is distributed in a large region in Eurasia, extending from Scandinavia and Central Europe to Central Asia, southern Siberia and South Asia. While one genetic study indicates that R1a originated 25,000 years ago, its subclade M417 (R1a1a1) diversified c. 5,800 years ago. The place of origin of the subclade plays a role in the debate about the origins of Proto-Indo-Europeans.
