Laplace operatorIn mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols , (where is the nabla operator), or . In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical and spherical coordinates, the Laplacian also has a useful form.
Laplace transformIn mathematics, the 'Laplace transform, named after its discoverer Pierre-Simon Laplace (ləˈplɑ:s), is an integral transform that converts a function of a real variable (usually , in the time domain) to a function of a complex variable (in the complex frequency domain, also known as s-domain', or s-plane). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms ordinary differential equations into algebraic equations and convolution into multiplication.
Laplace's equationIn mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as or where is the Laplace operator, is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.
Pierre-Simon LaplacePierre-Simon, Marquis de Laplace (ləˈplɑ:s; pjɛʁ simɔ̃ laplas; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized and extended the work of his predecessors in his five-volume Mécanique céleste (Celestial Mechanics) (1799–1825). This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems.
Romance languagesThe Romance languages, sometimes referred to as Latin languages or Neo-Latin languages, are numerous modern languages that evolved from Late Latin and its spoken form, often called Vulgar Latin. They are the only extant subgroup of the Italic languages branch of the Indo-European language family. The five most widely spoken Romance languages by number of native speakers are Spanish (489 million), Portuguese (283 million), French (80 million), Italian (67 million) and Romanian (24 million), which are all national languages of their respective countries of origin.
English orthographyEnglish orthography is the writing system used to represent spoken English, allowing readers to connect the graphemes to sound and to meaning. It includes English's norms of spelling, hyphenation, capitalisation, word breaks, emphasis, and punctuation. Like the orthography of most world languages, English orthography has a broad degree of standardisation. This standardisation began to develop when movable type spread to England in the late 15th century.
Tocharian languagesThe Tocharian (sometimes Tokharian) languages (təˈkɛəriən or təˈkɑːriən), also known as Arśi-Kuči, Agnean-Kuchean or Kuchean-Agnean, are an extinct branch of the Indo-European language family spoken by inhabitants of the Tarim Basin, the Tocharians. The languages are known from manuscripts dating from the 5th to the 8th century AD, which were found in oasis cities on the northern edge of the Tarim Basin (now part of Xinjiang in Northwest China) and the Lop Desert.
X-rayX-ray radiation, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz (3e16Hz to 3e19Hz) and energies in the range 124 keV to 145 eV, respectively. X-ray wavelengths are shorter than those of UV rays and typically longer than those of gamma rays.
X-ray tubeAn X-ray tube is a vacuum tube that converts electrical input power into X-rays. The availability of this controllable source of X-rays created the field of radiography, the imaging of partly opaque objects with penetrating radiation. In contrast to other sources of ionizing radiation, X-rays are only produced as long as the X-ray tube is energized. X-ray tubes are also used in CT scanners, airport luggage scanners, X-ray crystallography, material and structure analysis, and for industrial inspection.
SurfaceA surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".
V-2 rocketThe V-2 (Vergeltungswaffe 2), with the technical name Aggregat 4 (A-4), was the world's first long-range guided ballistic missile. The missile, powered by a liquid-propellant rocket engine, was developed during the Second World War in Nazi Germany as a "vengeance weapon" and assigned to attack Allied cities as retaliation for the Allied bombings of German cities. The V-2 rocket also became the first artificial object to travel into space by crossing the Kármán line (edge of space) with the vertical launch of MW 18014 on 20 June 1944.
Surface tensionSurface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to float on a water surface without becoming even partly submerged. At liquid–air interfaces, surface tension results from the greater attraction of liquid molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). There are two primary mechanisms in play.
DevanagariDevanāgarī or Devanagari (ˌdeɪvəˈnɑːɡəri ; देवनागरी, , Sanskrit pronunciation: deːʋɐˈnaːɡɐriː), also called Nāgarī (), is a left-to-right abugida (a type of segmental writing system), based on the ancient Brāhmī script, used in the northern Indian subcontinent. It is one of the official scripts of the Republic of India and Nepal. It was developed and in regular use by the 7th century CE. The Devanāgarī script, composed of 48 primary characters, including 14 vowels and 34 consonants, is the fourth most widely adopted writing system in the world, being used for over 120 languages.
Windows NTWindows NT is a proprietary graphical operating system produced by Microsoft, the first version of which was released on July 27, 1993. It is a processor-independent, multiprocessing and multi-user operating system. The first version of Windows NT was Windows NT 3.1 and was produced for workstations and server computers. It was a commercially focused operating system intended to complement consumer versions of Windows that were based on MS-DOS (including Windows 1.0 through Windows 3.1x).
Windows NT 4.0Windows NT 4.0 is a major release of the Windows NT operating system developed by Microsoft and oriented towards businesses. It is the direct successor to Windows NT 3.51, and was released to manufacturing on July 31, 1996, and then to retail in September 1996. It was Microsoft's primary business-oriented operating system until the introduction of Windows 2000. Workstation, server and embedded editions were sold, and all editions feature a graphical user interface similar to that of Windows 95, which was superseded by Windows 98 and could still be directly upgraded by either Windows 2000 Professional or Windows Me.
X86-64x86-64 (also known as x64, x86_64, AMD64, and Intel 64) is a 64-bit version of the x86 instruction set, first released in 1999. It introduced two new modes of operation, 64-bit mode and compatibility mode, along with a new 4-level paging mode. With 64-bit mode and the new paging mode, it supports vastly larger amounts of virtual memory and physical memory than was possible on its 32-bit predecessors, allowing programs to store larger amounts of data in memory.
V-1 flying bombThe V-1 flying bomb (Vergeltungswaffe 1 "Vengeance Weapon 1") was an early cruise missile. Its official Reich Aviation Ministry ( ()) designation was Fi 103. It was also known to the Allies as the buzz bomb or doodlebug and in Germany as Kirschkern (cherry stone) or Maikäfer (maybug). The V-1 was the first of the Vergeltungswaffen (V-weapons) deployed for the terror bombing of London. It was developed at Peenemünde Army Research Center in 1939 by the Luftwaffe at the beginning of the Second World War, and during initial development was known by the codename "Cherry Stone".
Windows NT 3.1Windows NT 3.1 is the first major release of the Windows NT operating system developed by Microsoft, released on July 27, 1993. At the time of Windows NT's release, Microsoft's Windows 3.1 desktop environment had established brand recognition and market share; but Windows 3.1 relied on the DOS operating system for essential functions, and it had a constrictive 16-bit architecture. Windows NT, however, was a complete, 32-bit operating system that retained a desktop environment familiar to Windows 3.1 users.
Gujarati scriptThe Gujarati script (ગુજરાતી લિપિ, transliterated: ) is an abugida for the Gujarati language, Kutchi language, and various other languages. It is one of the official scripts of the Indian Republic. It is a variant of the Devanagari script differentiated by the loss of the characteristic horizontal line running above the letters and by a number of modifications to some characters. Gujarati numerical digits are also different from their Devanagari counterparts.
Surface (topology)In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
