Complex planeIn mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
Phase-contrast X-ray imagingPhase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of the X-ray beam's intensity (attenuation) when traversing the sample, which can be measured directly with the assistance of an X-ray detector.
Differential of a functionIn calculus, the differential represents the principal part of the change in a function with respect to changes in the independent variable. The differential is defined by where is the derivative of f with respect to , and is an additional real variable (so that is a function of and ). The notation is such that the equation holds, where the derivative is represented in the Leibniz notation , and this is consistent with regarding the derivative as the quotient of the differentials.
Differential (mathematics)In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity.
Henri PoincaréJules Henri Poincaré (UKˈpwæ̃kɑreɪ, ; ɑ̃ʁi pwɛ̃kaʁe; 29 April 1854 - 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics.
Index fundAn index fund (also index tracker) is a mutual fund or exchange-traded fund (ETF) designed to follow certain preset rules so that the fund can replicate the performance ("track") of a specified basket of underlying investments. While index providers often emphasize that they are for-profit organizations, index providers have the ability to act as "reluctant regulators" when determining which companies are suitable for an index.
Parabolic trajectoryIn astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return.
Hyperbolic trajectoryIn astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.
Radial trajectoryIn astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards or away from each other in a straight line. There are three types of radial trajectories (orbits). Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. The relative speed of the two objects is less than the escape velocity.
Stock market indexIn finance, a stock index, or stock market index, is an index that measures the performance of a stock market, or of a subset of a stock market. It helps investors compare current stock price levels with past prices to calculate market performance. Two of the primary criteria of an index are that it is investable and transparent: The methods of its construction are specified. Investors may be able to invest in a stock market index by buying an index fund, which is structured as either a mutual fund or an exchange-traded fund, and "track" an index.
Sign languageSign languages (also known as signed languages) are languages that use the visual-manual modality to convey meaning, instead of spoken words. Sign languages are expressed through manual articulation in combination with non-manual markers. Sign languages are full-fledged natural languages with their own grammar and lexicon. Sign languages are not universal and are usually not mutually intelligible, although there are also similarities among different sign languages.
Compact spaceIn mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.
