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The mineral olivine () is a magnesium iron silicate with the chemical formula . It is a type of nesosilicate or orthosilicate. The primary component of the Earth's upper mantle, it is a common mineral in Earth's subsurface, but weathers quickly on the surface. Olivine has many uses, such as the gemstone peridot (or chr... | Olivine | Wikipedia | 497 | 45159 | https://en.wikipedia.org/wiki/Olivine | Physical sciences | Silicate minerals | Earth science |
Translucent olivine is sometimes used as a gemstone called peridot (péridot, the French word for olivine). It is also called chrysolite (or chrysolithe, from the Greek words for gold and stone), though this name is now rarely used in the English language. Some of the finest gem-quality olivine has been obtained from a ... | Olivine | Wikipedia | 398 | 45159 | https://en.wikipedia.org/wiki/Olivine | Physical sciences | Silicate minerals | Earth science |
Mg-rich olivine is stable to pressures equivalent to a depth of about within Earth. Because it is thought to be the most abundant mineral in Earth's mantle at shallower depths, the properties of olivine have a dominant influence upon the rheology of that part of Earth and hence upon the solid flow that drives plate te... | Olivine | Wikipedia | 484 | 45159 | https://en.wikipedia.org/wiki/Olivine | Physical sciences | Silicate minerals | Earth science |
There are three distinct oxygen sites (marked O1, O2 and O3 in figure 1), two distinct metal sites (M1 and M2) and only one distinct silicon site. O1, O2, M2 and Si all lie on mirror planes, while M1 exists on an inversion center. O3 lies in a general position.
High-pressure polymorphs
At the high temperatures and pre... | Olivine | Wikipedia | 498 | 45159 | https://en.wikipedia.org/wiki/Olivine | Physical sciences | Silicate minerals | Earth science |
Because of its rapid weathering, olivine is rarely found in sedimentary rock.
Mining
Norway
Norway is the main source of olivine in Europe, particularly in an area stretching from Åheim to Tafjord, and from Hornindal to Flemsøy in the Sunnmøre district. There is also olivine in Eid municipality. About 50% of the wor... | Olivine | Wikipedia | 466 | 45159 | https://en.wikipedia.org/wiki/Olivine | Physical sciences | Silicate minerals | Earth science |
Peridot ( ), sometimes called chrysolite, is a yellow-green transparent variety of olivine. Peridot is one of the few gemstones that occur in only one color.
Peridot can be found in mafic and ultramafic rocks occurring in lava and peridotite xenoliths of the mantle. The gem occurs in silica-deficient rocks such as vol... | Peridot | Wikipedia | 436 | 45162 | https://en.wikipedia.org/wiki/Peridot | Physical sciences | Silicate minerals | Earth science |
The molecular structure of peridot consists of isomorphic olivine, silicate, magnesium and iron in an orthorhombic crystal system. In an alternative view, the atomic structure can be described as a hexagonal, close-packed array of oxygen ions with half of the octahedral sites occupied by magnesium or iron ions and one-... | Peridot | Wikipedia | 488 | 45162 | https://en.wikipedia.org/wiki/Peridot | Physical sciences | Silicate minerals | Earth science |
Peridot crystals have been collected from some pallasite meteorites. The most commonly studied pallasitic peridot belongs to the Indonesian Jeppara meteorite, but others exist such as the Brenham, Esquel, Fukang, and Imilac meteorites.
Pallasitic (extraterrestrial) peridot differs chemically from its earthbound counter... | Peridot | Wikipedia | 509 | 45162 | https://en.wikipedia.org/wiki/Peridot | Physical sciences | Silicate minerals | Earth science |
Cultural history
Peridot has been prized since the earliest civilizations for its claimed protective powers to drive away fears and nightmares, according to superstitions. There is a superstition that it carries the gift of "inner radiance", sharpening the mind and opening it to new levels of awareness and growth, hel... | Peridot | Wikipedia | 164 | 45162 | https://en.wikipedia.org/wiki/Peridot | Physical sciences | Silicate minerals | Earth science |
Orthoclase, or orthoclase feldspar (endmember formula KAlSi3O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture", because its two cleavage planes are at right angles to each other. It is a type of potassium feldspar, also known as K-feldspar. Th... | Orthoclase | Wikipedia | 453 | 45165 | https://en.wikipedia.org/wiki/Orthoclase | Physical sciences | Silicate minerals | Earth science |
Some intergrowths of orthoclase and albite have an attractive pale luster and are called moonstone when used in jewelry. Most moonstones are translucent and white, although grey and peach-colored varieties also occur. In gemology, their luster is called adularescence and is typically described as creamy or silvery whit... | Orthoclase | Wikipedia | 201 | 45165 | https://en.wikipedia.org/wiki/Orthoclase | Physical sciences | Silicate minerals | Earth science |
Microcline (KAlSi3O8) is an important igneous rock-forming tectosilicate mineral. It is a potassium-rich alkali feldspar. Microcline typically contains minor amounts of sodium. It is common in granite and pegmatites. Microcline forms during slow cooling of orthoclase; it is more stable at lower temperatures than ortho... | Microcline | Wikipedia | 477 | 45166 | https://en.wikipedia.org/wiki/Microcline | Physical sciences | Silicate minerals | Earth science |
As food additive
The chemical compound name is potassium aluminium silicate, and it is known as E number reference E555. It was the subject in 2018 of a Call for technical and toxicological data from the EFSA.
In 2008, it (along with other Aluminum compounds) was the subject of
a Scientific Opinion of the Panel on Fo... | Microcline | Wikipedia | 88 | 45166 | https://en.wikipedia.org/wiki/Microcline | Physical sciences | Silicate minerals | Earth science |
Plagioclase ( ) is a series of tectosilicate (framework silicate) minerals within the feldspar group. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a continuous solid solution series, more properly known as the plagioclase feldspar series. This was first shown by th... | Plagioclase | Wikipedia | 482 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
The ability of albite and anorthite to form solid solutions in any proportions at elevated temperature reflects the ease with which calcium and aluminium can substitute for sodium and silicon in the plagioclase crystal structure. Although a calcium ion has a charge of +2, versus +1 for a sodium ion, the two ions have v... | Plagioclase | Wikipedia | 433 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
The luster is vitreous to pearly and the diaphaneity is transparent to translucent. The tenacity is brittle, and the fracture is uneven or conchoidal, but the fracture is rarely observed due to the strong tendency of the mineral to cleave instead. At low temperature, the crystal structure belongs to the triclinic syste... | Plagioclase | Wikipedia | 424 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
The distinction between these minerals cannot easily be made in the field. The composition can be roughly determined by specific gravity, but accurate measurement requires chemical or optical tests. The composition in a crushed grain mount can be obtained by the Tsuboi method, which yields an accurate measurement of th... | Plagioclase | Wikipedia | 412 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
Labradorite is the characteristic feldspar of the more basic rock types such as gabbro or basalt. Labradorite frequently shows an iridescent display of colors due to light refracting within the lamellae of the crystal. It is named after Labrador, where it is a constituent of the intrusive igneous rock anorthosite which... | Plagioclase | Wikipedia | 353 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
The liquidus of plagioclase (the temperature at which the plagioclase first begins to crystallize) is about for olivine basalt, with a composition of 50.5 wt% silica; in andesite with a silica content of 60.7 wt%; and in dacite with a silica content of 69.9 wt%. These values are for dry magma. The liquidus is greatl... | Plagioclase | Wikipedia | 446 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
Classification of igneous rocks
Plagioclase is very important for the classification of crystalline igneous rocks. Generally, the more silica is present in the rock, the fewer the mafic minerals, and the more sodium-rich the plagioclase. Alkali feldspar appears as the silica content becomes high. Under the QAPF classi... | Plagioclase | Wikipedia | 496 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
At very high temperatures, plagioclase forms a solid solution with potassium feldspar, but this becomes highly unstable on cooling. The plagioclase separates from the potassium feldspar, a process called exsolution. The resulting rock, in which fine streaks of plagioclase (lamellae) are present in potassium feldspar, i... | Plagioclase | Wikipedia | 268 | 45168 | https://en.wikipedia.org/wiki/Plagioclase | Physical sciences | Silicate minerals | Earth science |
In computing, a process is the instance of a computer program that is being executed by one or many threads. There are many different process models, some of which are light weight, but almost all processes (even entire virtual machines) are rooted in an operating system (OS) process which comprises the program code, a... | Process (computing) | Wikipedia | 507 | 45178 | https://en.wikipedia.org/wiki/Process%20%28computing%29 | Technology | Operating systems | null |
In general, a computer system process consists of (or is said to own) the following resources:
An image of the executable machine code associated with a program.
Memory (typically some region of virtual memory); which includes the executable code, process-specific data (input and output), a call stack (to keep track ... | Process (computing) | Wikipedia | 488 | 45178 | https://en.wikipedia.org/wiki/Process%20%28computing%29 | Technology | Operating systems | null |
Processes are often called "tasks" in embedded operating systems. The sense of "process" (or task) is "something that takes up time", as opposed to "memory", which is "something that takes up space".
The above description applies to both processes managed by an operating system, and processes as defined by process cal... | Process (computing) | Wikipedia | 439 | 45178 | https://en.wikipedia.org/wiki/Process%20%28computing%29 | Technology | Operating systems | null |
When processes need to communicate with each other they must share parts of their address spaces or use other forms of inter-process communication (IPC).
For instance in a shell pipeline, the output of the first process needs to pass to the second one, and so on. Another example is a task that has been decomposed into ... | Process (computing) | Wikipedia | 443 | 45178 | https://en.wikipedia.org/wiki/Process%20%28computing%29 | Technology | Operating systems | null |
Shortly thereafter, the notion of a "program" was expanded to the notion of an "executing program and its context". The concept of a process was born, which also became necessary with the invention of re-entrant code. Threads came somewhat later. However, with the advent of concepts such as time-sharing, computer netwo... | Process (computing) | Wikipedia | 106 | 45178 | https://en.wikipedia.org/wiki/Process%20%28computing%29 | Technology | Operating systems | null |
{{DISPLAYTITLE:Lp space}}
In mathematics, the spaces are function spaces defined using a natural generalization of the -norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Rie... | Lp space | Wikipedia | 394 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
For all the -norms and maximum norm satisfy the properties of a "length function" (or norm), that is:
only the zero vector has zero length,
the length of the vector is positive homogeneous with respect to multiplication by a scalar (positive homogeneity), and
the length of the sum of two vectors is no larger than the ... | Lp space | Wikipedia | 483 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
The mathematical definition of the norm was established by Banach's Theory of Linear Operations. The space of sequences has a complete metric topology provided by the F-norm on the product metric:
The -normed space is studied in functional analysis, probability theory, and harmonic analysis.
Another function was ca... | Lp space | Wikipedia | 512 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
General ℓp-space
In complete analogy to the preceding definition one can define the space over a general index set (and ) as
where convergence on the right means that only countably many summands are nonzero (see also Unconditional convergence).
With the norm
the space becomes a Banach space.
In the case where i... | Lp space | Wikipedia | 447 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
For every positive the value under of a measurable function and its absolute value are always the same (that is, for all ) and so a measurable function belongs to if and only if its absolute value does. Because of this, many formulas involving -norms are stated only for non-negative real-valued functions. Conside... | Lp space | Wikipedia | 486 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
This normed quotient space is called and it is the subject of this article. We begin by defining the quotient vector space.
Given any the coset consists of all measurable functions that are equal to almost everywhere.
The set of all cosets, typically denoted by
forms a vector space with origin when vector add... | Lp space | Wikipedia | 442 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
Special cases
For the spaces are a special case of spaces; when are the natural numbers and is the counting measure. More generally, if one considers any set with the counting measure, the resulting space is denoted For example, is the space of all sequences indexed by the integers, and when defining the -nor... | Lp space | Wikipedia | 484 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
The only nonempty convex open set in is the entire space. Consequently, there are no nonzero continuous linear functionals on the continuous dual space is the zero space. In the case of the counting measure on the natural numbers (i.e. ), the bounded linear functionals on are exactly those that are bounded on , i.e.... | Lp space | Wikipedia | 475 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
This map coincides with the canonical embedding of into its bidual. Moreover, the map is onto, as composition of two onto isometries, and this proves reflexivity.
If the measure on is sigma-finite, then the dual of is isometrically isomorphic to (more precisely, the map corresponding to is an isometry from o... | Lp space | Wikipedia | 511 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
Suppose is an open set with Then for every Borel set contained in there exist a closed set and an open set such that
for every . Subsequently, there exists a Urysohn function on that is on and on with
If can be covered by an increasing sequence of open sets that have finite measure, then the space of –i... | Lp space | Wikipedia | 432 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
Hilbert spaces
Hilbert spaces are central to many applications, from quantum mechanics to stochastic calculus. The spaces and are both Hilbert spaces. In fact, by choosing a Hilbert basis i.e., a maximal orthonormal subset of or any Hilbert space, one sees that every Hilbert space is isometrically isomorphic to (s... | Lp space | Wikipedia | 482 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
Given a measure space and a locally convex space (here assumed to be complete), it is possible to define spaces of -integrable -valued functions on in a number of ways. One way is to define the spaces of Bochner integrable and Pettis integrable functions, and then endow them with locally convex TVS-topologies that a... | Lp space | Wikipedia | 480 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
where is bounded continuous concave and non-decreasing on with and when (for example, Such a metric is called Lévy-metric for Under this metric the space is complete. However, as mentioned above, scalar multiplication is continuous with respect to this metric only if . To see this, consider the Lebesgue measura... | Lp space | Wikipedia | 134 | 45194 | https://en.wikipedia.org/wiki/Lp%20space | Mathematics | Mathematical analysis | null |
In mathematics, an injective function (also known as injection, or one-to-one function ) is a function that maps distinct elements of its domain to distinct elements of its codomain; that is, implies (equivalently by contraposition, implies ). In other words, every element of the function's codomain is the image o... | Injective function | Wikipedia | 323 | 45196 | https://en.wikipedia.org/wiki/Injective%20function | Mathematics | Functions: General | null |
Examples
For visual examples, readers are directed to the gallery section.
For any set and any subset the inclusion map (which sends any element to itself) is injective. In particular, the identity function is always injective (and in fact bijective).
If the domain of a function is the empty set, then the func... | Injective function | Wikipedia | 498 | 45196 | https://en.wikipedia.org/wiki/Injective%20function | Mathematics | Functions: General | null |
More generally, injective partial functions are called partial bijections.
Other properties
If and are both injective then is injective.
If is injective, then is injective (but need not be).
is injective if and only if, given any functions whenever then In other words, injective functions are precisely... | Injective function | Wikipedia | 424 | 45196 | https://en.wikipedia.org/wiki/Injective%20function | Mathematics | Functions: General | null |
There are multiple other methods of proving that a function is injective. For example, in calculus if is a differentiable function defined on some interval, then it is sufficient to show that the derivative is always positive or always negative on that interval. In linear algebra, if is a linear transformation it i... | Injective function | Wikipedia | 152 | 45196 | https://en.wikipedia.org/wiki/Injective%20function | Mathematics | Functions: General | null |
A submarine communications cable is a cable laid on the seabed between land-based stations to carry telecommunication signals across stretches of ocean and sea. The first submarine communications cables were laid beginning in the 1850s and carried telegraphy traffic, establishing the first instant telecommunications li... | Submarine communications cable | Wikipedia | 372 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Another insulating gum which could be melted by heat and readily applied to wire made its appearance in 1842. Gutta-percha, the adhesive juice of the Palaquium gutta tree, was introduced to Europe by William Montgomerie, a Scottish surgeon in the service of the British East India Company. Twenty years earlier, Montgome... | Submarine communications cable | Wikipedia | 476 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
In 1858, the steamship Elba was used to lay a telegraph cable from Jersey to Guernsey, on to Alderney and then to Weymouth, the cable being completed successfully in September of that year. Problems soon developed with eleven breaks occurring by 1860 due to storms, tidal and sand movements, and wear on rocks. A report ... | Submarine communications cable | Wikipedia | 421 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
British officials believed that depending on telegraph lines that passed through non-British territory posed a security risk, as lines could be cut and messages could be interrupted during wartime. They sought the creation of a worldwide network within the empire, which became known as the All Red Line, and conversely ... | Submarine communications cable | Wikipedia | 376 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Throughout the 1860s and 1870s, British cable expanded eastward, into the Mediterranean Sea and the Indian Ocean. An 1863 cable to Bombay (now Mumbai), India, provided a crucial link to Saudi Arabia. In 1870, Bombay was linked to London via submarine cable in a combined operation by four cable companies, at the behest ... | Submarine communications cable | Wikipedia | 487 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Transatlantic cables of the 19th century consisted of an outer layer of iron and later steel wire, wrapping India rubber, wrapping gutta-percha, which surrounded a multi-stranded copper wire at the core. The portions closest to each shore landing had additional protective armour wires. Gutta-percha, a natural polymer s... | Submarine communications cable | Wikipedia | 388 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Many early cables suffered from attack by sea life. The insulation could be eaten, for instance, by species of Teredo (shipworm) and Xylophaga. Hemp laid between the steel wire armouring gave pests a route to eat their way in. Damaged armouring, which was not uncommon, also provided an entrance. Cases of sharks biting ... | Submarine communications cable | Wikipedia | 506 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Early cable designs failed to analyse these effects correctly. Famously, E.O.W. Whitehouse had dismissed the problems and insisted that a transatlantic cable was feasible. When he subsequently became chief electrician of the Atlantic Telegraph Company, he became involved in a public dispute with William Thomson. Whiteh... | Submarine communications cable | Wikipedia | 482 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
In the 1960s, transoceanic cables were coaxial cables that transmitted frequency-multiplexed voiceband signals. A high-voltage direct current on the inner conductor powered repeaters (two-way amplifiers placed at intervals along the cable). The first-generation repeaters remain among the most reliable vacuum tube ampli... | Submarine communications cable | Wikipedia | 399 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Repeaters are powered by a constant direct current passed down the conductor near the centre of the cable, so all repeaters in a cable are in series. Power feed equipment (PFE) is installed at the terminal stations. Typically both ends share the current generation with one end providing a positive voltage and the other... | Submarine communications cable | Wikipedia | 417 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Originally, submarine cables were simple point-to-point connections. With the development of submarine branching units (SBUs), more than one destination could be served by a single cable system. Modern cable systems now usually have their fibers arranged in a self-healing ring to increase their redundancy, with the sub... | Submarine communications cable | Wikipedia | 344 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Switching and all-by-sea routing commonly increases the distance and thus the round trip latency by more than 50%. For example, the round trip delay (RTD) or latency of the fastest transatlantic connections is under 60 ms, close to the theoretical optimum for an all-sea route. While in theory, a great circle route (GCP... | Submarine communications cable | Wikipedia | 403 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Optical post amplifiers, used to increase the strength of the signal generated by the optical transmitter often use a diode-pumped erbium-doped fiber laser. The diode is often a high power 980 or 1480 nm laser diode. This setup allows for an amplification of up to +24dBm in an affordable manner. Using an erbium-ytterbi... | Submarine communications cable | Wikipedia | 423 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
WDM or wavelength division multiplexing was first implemented in submarine fiber optic cables from the 1990s to the 2000s, followed by DWDM or dense wavelength division mulltiplexing around 2007. Each fiber can carry 30 wavelengths at a time. SDM or spatial division multiplexing submarine cables have at least 12 fiber ... | Submarine communications cable | Wikipedia | 469 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Most cables in the 20th century crossed the Atlantic Ocean, to connect the United States and Europe. However, capacity in the Pacific Ocean was much expanded starting in the 1990s. For example, between 1998 and 2003, approximately 70% of undersea fiber-optic cable was laid in the Pacific. This is in part a response ... | Submarine communications cable | Wikipedia | 465 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Importance of submarine cables
Submarine cables, while often perceived as ‘insignificant’ parts of communication infrastructure as they lay “hidden” in the seabed, are an essential infrastructure in the digital era, carrying 99% of the data traffic across the oceans. This data includes all internet traffic, military t... | Submarine communications cable | Wikipedia | 483 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
The U.S military, for example, uses the submarine cable network for data transfer from conflict zones to command staff in the United States (U.S.). Interruption of the cable network during intense operations could have direct consequences for the military on the ground.
The criticality of cable services makes their ge... | Submarine communications cable | Wikipedia | 483 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
The cables' vulnerability is further compounded by technological advancements, such as the development of Unmanned Underwater Vehicles (UUVs), which enable covert cable damage while avoiding detection. However, even low-tech attacks can impact the cable's security significantly, as demonstrated in 2013, when three dive... | Submarine communications cable | Wikipedia | 497 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
A cable repair ship will be sent to the location to drop a marker buoy near the break. Several types of grapples are used depending on the situation. If the sea bed in question is sandy, a grapple with rigid prongs is used to plough under the surface and catch the cable. If the cable is on a rocky sea surface, the grap... | Submarine communications cable | Wikipedia | 463 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Cyber espionage and Intelligence-gathering
The rising sophistication of cyberattacks underscores the vulnerability of submarine cables to cyberespionage, ultimately complicating their security. Techniques like cable tapping, hacking into network management systems, and targeting cable landing stations enable covert da... | Submarine communications cable | Wikipedia | 476 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Some scholars advocate for heightened European Union (E.U.) coordination, recommending improvements in surveillance and response capabilities across various agencies, such as the Coast Guard and specific telecommunication regulators. Given the central role of private companies in cable ownership, some experts also unde... | Submarine communications cable | Wikipedia | 448 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
These tactics elevate cable security to a significant geopolitical issue. Criminal actors may further target cables as a means of economic warfare, aiming to destabilize economies or convey political messages. The disruption of submarine communication cables in highly politicised maritime areas thus has a significant p... | Submarine communications cable | Wikipedia | 483 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
However, submarine cables face significant legal challenges and lack specific legal protection in UNCLOS and enforcement mechanisms against emerging threats, particular in international waters. This is further complicated by the non-ratification of the treaty by key states such as the U.S. and Turkey. Many countries la... | Submarine communications cable | Wikipedia | 509 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Alteration of the seabed
Seabed ecosystems can be disturbed by the installation and maintenance of cables. The effects of cable installation are generally limited to specific areas. The intensity of disturbance depends on the installation method.
Cables are often laid in the so-called benthic zone of the seabed. The ... | Submarine communications cable | Wikipedia | 469 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
Areas with a high density of submarine cables have the advantage of being safer from fishing. At the expense of benthic and sedimentary zones, marine fauna is better protected in these maritime regions, thanks to limitations and bans. Studies have shown a positive effect on the fauna surrounding cable installation zone... | Submarine communications cable | Wikipedia | 366 | 45206 | https://en.wikipedia.org/wiki/Submarine%20communications%20cable | Technology | Telecommunications | null |
A communications satellite is an artificial satellite that relays and amplifies radio telecommunication signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth. Communications satellites are used for television, telephone, radio, internet... | Communications satellite | Wikipedia | 482 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Early active and passive satellite experiments
There are two major classes of communications satellites, passive and active. Passive satellites only reflect the signal coming from the source, toward the direction of the receiver. With passive satellites, the reflected signal is not amplified at the satellite, and only... | Communications satellite | Wikipedia | 444 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
NASA's satellite applications program launched the first artificial satellite used for passive relay communications in Echo 1 on 12 August 1960. Echo 1 was an aluminized balloon satellite acting as a passive reflector of microwave signals. Communication signals were bounced off the satellite from one point on Earth to ... | Communications satellite | Wikipedia | 479 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
In the United States, 1962 saw the creation of the Communications Satellite Corporation (COMSAT) private corporation, which was subject to instruction by the US Government on matters of national policy. Over the next two years, international negotiations led to the Intelsat Agreements, which in turn led to the launch o... | Communications satellite | Wikipedia | 364 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Communications satellites usually have one of three primary types of orbit, while other orbital classifications are used to further specify orbital details. MEO and LEO are non-geostationary orbit (NGSO).
Geostationary satellites have a geostationary orbit (GEO), which is from Earth's surface. This orbit has the spec... | Communications satellite | Wikipedia | 445 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Low-Earth-orbiting satellites are less expensive to launch into orbit than geostationary satellites and, due to proximity to the ground, do not require as high signal strength (signal strength falls off as the square of the distance from the source, so the effect is considerable). Thus there is a trade off between the ... | Communications satellite | Wikipedia | 469 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Examples of MEO
In 1962, the communications satellite, Telstar, was launched. It was a medium Earth orbit satellite designed to help facilitate high-speed telephone signals. Although it was the first practical way to transmit signals over the horizon, its major drawback was soon realised. Because its orbital period o... | Communications satellite | Wikipedia | 281 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Examples of GEO
The first geostationary satellite was Syncom 3, launched on 19 August 1964, and used for communication across the Pacific starting with television coverage of the 1964 Summer Olympics. Shortly after Syncom 3, Intelsat I, aka Early Bird, was launched on 6 April 1965 and placed in orbit at 28° west long... | Communications satellite | Wikipedia | 460 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Geostationary satellites must operate above the equator and therefore appear lower on the horizon as the receiver gets farther from the equator. This will cause problems for extreme northerly latitudes, affecting connectivity and causing multipath interference (caused by signals reflecting off the ground and into the g... | Communications satellite | Wikipedia | 448 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
These orbits are Sun synchronous, meaning that they cross the equator at the same local time each day. For example, the satellites in the NPOESS (civilian) orbit will cross the equator, going from south to north, at times 1:30 P.M., 5:30 P.M., and 9:30 P.M.
Beyond geostationary orbit
There are plans and initiatives t... | Communications satellite | Wikipedia | 431 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Frequency allocation for satellite systems
Allocating frequencies to satellite services is a complicated process which requires international coordination and planning. This is carried out under the auspices of the International Telecommunication Union (ITU).
To facilitate frequency planning, the world is divided into... | Communications satellite | Wikipedia | 494 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
As television became the main market, its demand for simultaneous delivery of relatively few signals of large bandwidth to many receivers being a more precise match for the capabilities of geosynchronous comsats. Two satellite types are used for North American television and radio: Direct broadcast satellite (DBS), an... | Communications satellite | Wikipedia | 402 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
A direct broadcast satellite is a communications satellite that transmits to small DBS satellite dishes (usually 18 to 24 inches or 45 to 60 cm in diameter). Direct broadcast satellites generally operate in the upper portion of the microwave Ku band. DBS technology is used for DTH-oriented (Direct-To-Home) satellite TV... | Communications satellite | Wikipedia | 503 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
Amateur radio operators have access to amateur satellites, which have been designed specifically to carry amateur radio traffic. Most such satellites operate as spaceborne repeaters, and are generally accessed by amateurs equipped with UHF or VHF radio equipment and highly directional antennas such as Yagis or dish ant... | Communications satellite | Wikipedia | 393 | 45207 | https://en.wikipedia.org/wiki/Communications%20satellite | Technology | Media and communication | null |
In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation is denoted multiplicatively, where the kernel is the inverse image of 1). An important special case is the kernel of a linear map. The kernel of a matrix, also called t... | Kernel (algebra) | Wikipedia | 494 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
The kernel ker T is always a linear subspace of V. Thus, it makes sense to speak of the quotient space . The first isomorphism theorem for vector spaces states that this quotient space is naturally isomorphic to the image of T (which is a subspace of W). As a consequence, the dimension of V equals the dimension of the ... | Kernel (algebra) | Wikipedia | 447 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
The homomorphism f is injective if and only if its kernel is only the singleton set {eG}. If f were not injective, then the non-injective elements can form a distinct element of its kernel: there would exist such that and . Thus . f is a group homomorphism, so inverses and group operations are preserved, giving ; in ... | Kernel (algebra) | Wikipedia | 450 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
Since ker f contains the multiplicative identity only when S is the zero ring, it turns out that the kernel is generally not a subring of R. The kernel is a subrng, and, more precisely, a two-sided ideal of R.
Thus, it makes sense to speak of the quotient ring .
The first isomorphism theorem for rings states that this ... | Kernel (algebra) | Wikipedia | 496 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
General case
Let A and B be algebraic structures of a given type and let f be a homomorphism of that type from A to B.
Then the kernel of f is the subset of the direct product consisting of all those ordered pairs of elements of A whose components are both mapped by f to the same element in B.
The kernel is usually d... | Kernel (algebra) | Wikipedia | 486 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
The notion of ideal generalises to any Malcev algebra (as linear subspace in the case of vector spaces, normal subgroup in the case of groups, two-sided ideals in the case of rings, and submodule in the case of modules).
It turns out that ker f is not a subalgebra of A, but it is an ideal.
Then it makes sense to speak... | Kernel (algebra) | Wikipedia | 502 | 45240 | https://en.wikipedia.org/wiki/Kernel%20%28algebra%29 | Mathematics | Abstract algebra | null |
In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and other algebraic ... | Isomorphism theorems | Wikipedia | 426 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
Let be a group. Let be a subgroup of , and let be a normal subgroup of . Then the following hold:
The product is a subgroup of ,
The subgroup is a normal subgroup of ,
The intersection is a normal subgroup of , and
The quotient groups and are isomorphic.
Technically, it is not necessary for to be a norma... | Isomorphism theorems | Wikipedia | 452 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
The first isomorphism theorem can be expressed in category theoretical language by saying that the category of groups is (normal epi, mono)-factorizable; in other words, the normal epimorphisms and the monomorphisms form a factorization system for the category. This is captured in the commutative diagram in the margin... | Isomorphism theorems | Wikipedia | 447 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
Note on numbers and names
Below we present four theorems, labelled A, B, C and D. They are often numbered as "First isomorphism theorem", "Second..." and so on; however, there is no universal agreement on the numbering. Here we give some examples of the group isomorphism theorems in the literature. Notice that these t... | Isomorphism theorems | Wikipedia | 466 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
Modules
The statements of the isomorphism theorems for modules are particularly simple, since it is possible to form a quotient module from any submodule. The isomorphism theorems for vector spaces (modules over a field) and abelian groups (modules over ) are special cases of these. For finite-dimensional vector spa... | Isomorphism theorems | Wikipedia | 492 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
A congruence on an algebra is an equivalence relation that forms a subalgebra of considered as an algebra with componentwise operations. One can make the set of equivalence classes into an algebra of the same type by defining the operations via representatives; this will be well-defined since is a subalgebra of .... | Isomorphism theorems | Wikipedia | 339 | 45241 | https://en.wikipedia.org/wiki/Isomorphism%20theorems | Mathematics | Abstract algebra | null |
In the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines occur. The goal of this interaction is to allow effective operation and control of the machine from the human end, while the machine simultaneously feeds back information that ... | User interface | Wikipedia | 417 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
Composite user interfaces (CUIs) are UIs that interact with two or more senses. The most common CUI is a graphical user interface (GUI), which is composed of a tactile UI and a visual UI capable of displaying graphics. When sound is added to a GUI, it becomes a multimedia user interface (MUI). There are three broad cat... | User interface | Wikipedia | 457 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
Tools used for incorporating human factors in the interface design are developed based on knowledge of computer science, such as computer graphics, operating systems, programming languages. Nowadays, we use the expression graphical user interface for human–machine interface on computers, as nearly all of them are now u... | User interface | Wikipedia | 495 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
In some circumstances, computers might observe the user and react according to their actions without specific commands. A means of tracking parts of the body is required, and sensors noting the position of the head, direction of gaze and so on have been used experimentally. This is particularly relevant to immersive in... | User interface | Wikipedia | 476 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
Early batch systems gave the currently running job the entire computer; program decks and tapes had to include what we would now think of as operating system code to talk to I/O devices and do whatever other housekeeping was needed. Midway through the batch period, after 1957, various groups began to experiment with so... | User interface | Wikipedia | 407 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
The widespread adoption of video-display terminals (VDTs) in the mid-1970s ushered in the second phase of command-line systems. These cut latency further, because characters could be thrown on the phosphor dots of a screen more quickly than a printer head or carriage can move. They helped quell conservative resistance ... | User interface | Wikipedia | 377 | 45249 | https://en.wikipedia.org/wiki/User%20interface | Technology | User interface | null |
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