Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
French ResistanceThe French Resistance (La Résistance) was a collection of organizations that fought the Nazi occupation of France and the collaborationist Vichy régime in France during the Second World War. Resistance cells were small groups of armed men and women (called the Maquis in rural areas) who conducted guerrilla warfare and published underground newspapers. They also provided first-hand intelligence information, and escape networks that helped Allied soldiers and airmen trapped behind Axis enemy lines.
Complex numberIn mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the , and b is called the . The set of complex numbers is denoted by either of the symbols or C.
Impact eventAn impact event is a collision between astronomical objects causing measurable effects. Impact events have physical consequences and have been found to regularly occur in planetary systems, though the most frequent involve asteroids, comets or meteoroids and have minimal effect. When large objects impact terrestrial planets such as the Earth, there can be significant physical and biospheric consequences, though atmospheres mitigate many surface impacts through atmospheric entry.
Charge-coupled deviceA charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a major technology used in digital imaging. In a CCD , pixels are represented by p-doped metal–oxide–semiconductor (MOS) capacitors.
Connection formIn mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object.
Impact craterAn impact crater is a circular depression in the surface of a solid astronomical object formed by the hypervelocity impact of a smaller object. In contrast to volcanic craters, which result from explosion or internal collapse, impact craters typically have raised rims and floors that are lower in elevation than the surrounding terrain. Lunar impact craters range from microscopic craters on lunar rocks returned by the Apollo program and small, simple, bowl-shaped depressions in the lunar regolith to large, complex, multi-ringed impact basins.
Carrier waveIn telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal (called the message signal or modulation signal) for the purpose of conveying information. This carrier wave usually has a much higher frequency than the message signal does. This is because it is impractical to transmit signals with low frequencies.
Computational biologyComputational biology refers to the use of data analysis, mathematical modeling and computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and big data, the field also has foundations in applied mathematics, chemistry, and genetics. It differs from biological computing, a subfield of computer engineering which uses bioengineering to build computers. Bioinformatics, the analysis of informatics processes in biological systems, began in the early 1970s.
Complex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
