Matrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .
11 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.
X-ray astronomyX-ray astronomy is an observational branch of astronomy which deals with the study of X-ray observation and detection from astronomical objects. X-radiation is absorbed by the Earth's atmosphere, so instruments to detect X-rays must be taken to high altitude by balloons, sounding rockets, and satellites. X-ray astronomy uses a type of space telescope that can see x-ray radiation which standard optical telescopes, such as the Mauna Kea Observatories, cannot.
44 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern.
T-carrierThe T-carrier is a member of the series of carrier systems developed by AT&T Bell Laboratories for digital transmission of multiplexed telephone calls. The first version, the Transmission System 1 (T1), was introduced in 1962 in the Bell System, and could transmit up to 24 telephone calls simultaneously over a single transmission line of copper wire. Subsequent specifications carried multiples of the basic T1 (1.544 Mbit/s) data rates, such as T2 (6.312 Mbit/s) with 96 channels, T3 (44.
Digital Signal 1Digital Signal 1 (DS1, sometimes DS-1) is a T-carrier signaling scheme devised by Bell Labs. DS1 is the primary digital telephone standard used in the United States, Canada and Japan and is able to transmit up to 24 multiplexed voice and data calls over telephone lines. E-carrier is used in place of T-carrier outside the United States, Canada, Japan, and South Korea. DS1 is the logical bit pattern used over a physical T1 line; in practice, the terms DS1 and T1 are often used interchangeably.
XenonXenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the formation of xenon hexafluoroplatinate, the first noble gas compound to be synthesized. Xenon is used in flash lamps and arc lamps, and as a general anesthetic. The first excimer laser design used a xenon dimer molecule (Xe2) as the lasing medium, and the earliest laser designs used xenon flash lamps as pumps.
Xenon difluorideXenon difluoride is a powerful fluorinating agent with the chemical formula XeF2, and one of the most stable xenon compounds. Like most covalent inorganic fluorides it is moisture-sensitive. It decomposes on contact with water vapor, but is otherwise stable in storage. Xenon difluoride is a dense, colourless crystalline solid. It has a nauseating odour and low vapor pressure. Xenon difluoride is a linear molecule with an Xe–F bond length of 197.73pm in the vapor stage, and 200 pm in the solid phase.
PerxenateIn chemistry, perxenates are salts of the yellow xenon-containing anion XeO64-. This anion has octahedral molecular geometry, as determined by Raman spectroscopy, having O–Xe–O bond angles varying between 87° and 93°. The Xe–O bond length was determined by X-ray crystallography to be 1.875 Å. Perxenates are synthesized by the disproportionation of xenon trioxide when dissolved in strong alkali: 2 XeO3 ( ()) + 4 OH− ( ()) → Xe ( ()) + XeO64- ( ()) + O2 ( ()) + 2 H2O ( ()) When Ba(OH)2 is used as the alkali, barium perxenate can be crystallized from the resulting solution.
Exponential functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers.
MacOSmacOS (ˌmækoʊˈɛs; previously OS X and originally Mac OS X) is an operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and laptop computers, it is the second most widely used desktop OS, after Microsoft Windows and ahead of Linux (including ChromeOS). macOS succeeded the classic Mac OS, a Mac operating system with nine releases from 1984 to 1999.
