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Parabolic Coords
Parabolic usually refers to something in a shape of a parabola, but may also refer to a parable. Parabolic may refer to: *In mathematics: **In elementary mathematics, especially elementary geometry: **Parabolic coordinates **Parabolic cylindrical coordinates **Möbius transformation#Parabolic transforms, parabolic Möbius transformation **Parabolic geometry (other) **Fermat's spiral, Parabolic spiral **Parabolic line **In advanced mathematics: ***Parabolic cylinder function ***Parabolic induction ***Parabolic Lie algebra ***Parabolic partial differential equation *In physics: **Parabolic trajectory *In technology: **Parabolic antenna **Parabolic microphone **Parabolic reflector **Parabolic trough - a type of solar thermal energy collector **Parabolic flight - a way of achieving weightlessness **Fishing rod#Specifications, Parabolic action, or parabolic bending curve - a term often used to refer to a progressive bending curve in fishing rods. *In commodities and stock market ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Partial Differential Equation
A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent phenomena, including heat conduction, particle diffusion, and pricing of derivative investment instruments. Definition To define the simplest kind of parabolic PDE, consider a real-valued function u(x, y) of two independent real variables, x and y. A second-order, linear, constant-coefficient PDE for u takes the form :Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + F = 0, and this PDE is classified as being ''parabolic'' if the coefficients satisfy the condition :B^2 - AC = 0. Usually x represents one-dimensional position and y represents time, and the PDE is solved subject to prescribed initial and boundary conditions. The name "parabolic" is used because the assumption on the coefficients is the same as the condition for the analytic geometry equation A x^2 + 2B xy + C y^2 + D x + E y + F = 0 to define a planar parabola. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fishing Rod
A fishing rod is a long, thin rod used by angling, anglers to fishing, catch fish by manipulating a fishing line, line ending in a fish hook, hook (formerly known as an ''angle'', hence the term "angling"). At its most basic form, a fishing rod is a straight rigid stick/pole with a line attached to one end (as seen in traditional Tenkara fishing); however, modern rods are usually elastic and generally have the line stored in a fishing reel, reel mounted at the rod handle, which is hand-cranked and controls the line retrieval, as well as numerous line-restricting rings (also known as ''line guides'') that distribute bending stress along the rod and help dampening down/prevent line whipping and entanglement. To better entice fish, fishing bait, baits or fishing lure, lures are dressed onto the one or more hooks attached to the line, and a bite indicator is used, some of which (e.g. quiver tip) might be incorporated as part of the rod itself. Fishing rod acts as an extended leve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fishing Rod
A fishing rod is a long, thin rod used by angling, anglers to fishing, catch fish by manipulating a fishing line, line ending in a fish hook, hook (formerly known as an ''angle'', hence the term "angling"). At its most basic form, a fishing rod is a straight rigid stick/pole with a line attached to one end (as seen in traditional Tenkara fishing); however, modern rods are usually elastic and generally have the line stored in a fishing reel, reel mounted at the rod handle, which is hand-cranked and controls the line retrieval, as well as numerous line-restricting rings (also known as ''line guides'') that distribute bending stress along the rod and help dampening down/prevent line whipping and entanglement. To better entice fish, fishing bait, baits or fishing lure, lures are dressed onto the one or more hooks attached to the line, and a bite indicator is used, some of which (e.g. quiver tip) might be incorporated as part of the rod itself. Fishing rod acts as an extended leve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Flight
A reduced-gravity aircraft is a type of fixed-wing aircraft that provides brief near-weightless environments for training astronauts, conducting research and making gravity-free movie shots. Versions of such airplanes were operated by the NASA Reduced Gravity Research Program, and one is currently operated by the Human Spaceflight and Robotic Exploration Programmes of the European Space Agency. The unofficial nickname "vomit comet" became popular among those who experienced their operation. History Parabolic flight as a way of simulating weightlessness was first proposed by the German aerospace engineer Fritz Haber and the German physicist Heinz Haber in 1950. Both had been brought to the US after World War II as part of Operation Paperclip. As well, Shih-Chun Wang studied nausea in astronauts for NASA, which helped lead to the creation of the vomit comet. Parabolic flights are sometimes used to examine the effects of weightlessness on a living organism. While humans are b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Trough
A parabolic trough is a type of solar thermal collector that is straight in one dimension and curved as a parabola in the other two, lined with a polished metal mirror. The sunlight which enters the mirror parallel to its plane of symmetry is focused along the focal line, where objects are positioned that are intended to be heated. In a solar cooker, for example, food is placed at the focal line of a trough, which is cooked when the trough is aimed so the Sun is in its plane of symmetry. For other purposes, a tube containing a fluid runs the length of the trough at its focal line. The sunlight is concentrated on the tube and the fluid heated to a high temperature by the energy of the sunlight. The hot fluid can be piped to a heat engine, which uses the heat energy to drive machinery, or to generate electricity. This solar energy collector is the most common and best known type of parabolic trough. When heat transfer fluid is used to heat steam to drive a standard turbine generat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Reflector
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave travelling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis. Parabolic reflectors are used to collect energy from a distant source (for example sound waves or incoming star light). Since the principles of reflection are reversible, parabolic reflectors can also be used to collimate radiation from an isotropic source into a parallel beam. In optics, parabolic mirrors are used to gather light in reflecting telescopes and solar furnaces, and project a beam of light in flas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Microphone
A parabolic microphone is a microphone that uses a parabolic reflector to collect and focus sound waves onto a transducer, in much the same way that a parabolic antenna (e.g. satellite dish) does with radio waves. Though they lack high fidelity, parabolic microphones have great sensitivity to sounds coming from one direction, along the axis of the dish, and can pick up distant sounds. Limitations Parabolic microphones are generally not used for high fidelity applications because dishes small enough to be portable have poor low-frequency response. This is because, from the Rayleigh criterion, parabolic dishes can only focus waves with a wavelength much smaller than the diameter of their aperture. The wavelength of sound waves at the low end of human hearing (20 Hz) is about ; focusing them would require a dish much larger than this. A typical parabolic microphone dish with a diameter of one metre has little directivity for sound waves longer than 30 cm, correspondin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Antenna
A parabolic antenna is an antenna that uses a parabolic reflector, a curved surface with the cross-sectional shape of a parabola, to direct the radio waves. The most common form is shaped like a dish and is popularly called a dish antenna or parabolic dish. The main advantage of a parabolic antenna is that it has high directivity. It functions similarly to a searchlight or flashlight reflector to direct radio waves in a narrow beam, or receive radio waves from one particular direction only. Parabolic antennas have some of the highest gains, meaning that they can produce the narrowest beamwidths, of any antenna type. In order to achieve narrow beamwidths, the parabolic reflector must be much larger than the wavelength of the radio waves used, so parabolic antennas are used in the high frequency part of the radio spectrum, at UHF and microwave ( SHF) frequencies, at which the wavelengths are small enough that conveniently-sized reflectors can be used. Parabolic antennas are u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Trajectory
In 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. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits. Velocity The orbital velocity (v) of a body travelling along parabolic trajectory can be computed as: :v = \sqrt where: *r is the radial distance of orbiting body from central body, *\mu is the standard gravitational parameter. At any positi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabolic Lie Algebra
In algebra, a parabolic Lie algebra \mathfrak p is a subalgebra of a semisimple Lie algebra \mathfrak g satisfying one of the following two conditions: * \mathfrak p contains a maximal solvable subalgebra (a Borel subalgebra) of \mathfrak g; * the Killing perp of \mathfrak p in \mathfrak g is the nilradical of \mathfrak p. These conditions are equivalent over an algebraically closed field of characteristic zero, such as the complex numbers. If the field \mathbb F is not algebraically closed, then the first condition is replaced by the assumption that * \mathfrak p\otimes_\overline contains a Borel subalgebra of \mathfrak g\otimes_\overline where \overline is the algebraic closure of \mathbb F. See also * Generalized flag variety In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space ''V'' over a field F. When F is the real or complex numbers, a generalized flag variety is a smo ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parable
A parable is a succinct, didactic story, in prose or verse, that illustrates one or more instructive lessons or principles. It differs from a fable in that fables employ animals, plants, inanimate objects, or forces of nature as characters, whereas parables have human characters. A parable is a type of metaphorical analogy. Some scholars of the canonical gospels and the New Testament apply the term "parable" only to the parables of Jesus, although that is not a common restriction of the term. Parables such as the parable of the Prodigal Son are important to Jesus's teaching method. Etymology The word ''parable'' comes from the Greek παραβολή (''parabolē''), literally "throwing" (''bolē'') "alongside" (''para-''), by extension meaning "comparison, illustration, analogy." It was the name given by Greek rhetoricians to an illustration in the form of a brief fictional narrative. History The Bible contains numerous parables in the Gospels of the New Testament ( Jesus' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
