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In modern warfare, some vehicles used by police tactical units, counterterrorists, and special forces can be fitted with mechanical assault ladders with ramps. These are essentially modern siege towers with elements of escalade ladders, and are used to raid a structure through its upper levels. These assault ladders are not as large or as tall as their predecessors, and are typically only capable of reaching roughly the third or fourth floor of a structure. | https://en.wikipedia.org/wiki/Siege_towers |
On 1 March 2007, police officers entered Ungdomshuset in Copenhagen, Denmark using boom cranes in a manner similar to siege towers. The officers were placed in containers that the crane operators raised and placed against the structure's windows, from which the officers then entered. == See also == | https://en.wikipedia.org/wiki/Siege_towers |
In modern warfare, towed artillery has given way in part to self-propelled artillery. It is also common to find auxiliary power units built into the gun carriage to provide power while the propulsion engine is offline. Traditional towed artillery can still be found in units where complexity and weight are liabilities: e.g. airmobile, amphibious and other light units. | https://en.wikipedia.org/wiki/Artillery_tractor |
In such units, where organic transport is usually limited, any available transport can double as artillery tractors in order to reposition guns when needed. For example, engineer vehicles of a different primary purpose such as the U.S. Marines' Light Capacity Rough Terrain Forklift (LCRTF), a versatile telehandler forklift capable of towing gear from either end. | https://en.wikipedia.org/wiki/Artillery_tractor |
In modern western music (from the 18th century onward), the Phrygian mode is related to the modern natural minor scale, also known as the Aeolian mode, but with the second scale degree lowered by a semitone, making it a minor second above the tonic, rather than a major second. The following is the Phrygian mode starting on E, or E Phrygian, with corresponding tonal scale degrees illustrating how the modern major mode and natural minor mode can be altered to produce the Phrygian mode: Therefore, the Phrygian mode consists of: root, minor second, minor third, perfect fourth, perfect fifth, minor sixth, minor seventh, and octave. Alternatively, it can be written as the pattern half, whole, whole, whole, half, whole, wholeIn contemporary jazz, the Phrygian mode is used over chords and sonorities built on the mode, such as the sus4(♭9) chord (see Suspended chord), which is sometimes called a Phrygian suspended chord. For example, a soloist might play an E Phrygian over an Esus4(♭9) chord (E–A–B–D–F). | https://en.wikipedia.org/wiki/Phrygian_mode |
In modern western politics, some people believe that exclusive ownership of property underlies much social injustice, and facilitates tyranny and oppression on an individual and societal scale. Others consider the striving to achieve greater ownership of wealth as the driving factor behind human technological advancement and increasing standards of living. Some support the latter view, believing that ownership is necessary for liberty itself. | https://en.wikipedia.org/wiki/Right_of_ownership |
In modern wood carving, the style is also called spoon carving. The style is traditional in the folk art of many countries. Patterns can be free form style or based on geometric figures. In America it is mostly used with basswood, butternut, pine, or mahogany. Chip carving knives can also be used for whittling, cabinet making, and general workbench purposes. | https://en.wikipedia.org/wiki/Chip_carving |
In modern wood construction, sills usually come in sizes of 2×4, 2×6, 2×8, and 2×10. In stick framing, the sill is made of treated lumber, and is anchored to the foundation wall, often with J-bolts, to keep the building from coming off the foundation during a severe storm or earthquake. Building codes require that the bottom of the sill plate be kept 6 to 8 inches above the finished grade, to hinder termites, and to prevent the sill plate from rotting. | https://en.wikipedia.org/wiki/Sill_plate |
In modern world we use digital tools to improve the teaching-learning process. The most common tool we use in classroom these days is PowerPoint slides, which makes the class more interesting, dynamic and effective. Moreover it also helps to introduce new topics in easy way. | https://en.wikipedia.org/wiki/Audiovisual_education |
The use of audiovisual aids makes the students to remember the concept for longer period of time. They convey the same meaning as words but it gives clear concepts thus help to bring effectiveness in learning. Integrating technology into the classroom help students to experience things virtually or vicariously. | https://en.wikipedia.org/wiki/Audiovisual_education |
For example, if the teacher wants to give a lesson on Taj Mahal, it is possible that not all the students in India have visited the place but you can show it through a video thereby allowing the students to see the monument with their own eyes. Although the first hand experience is the best way of educative experience but such an experience cannot always be done practical so in some case we need to have substitution. Use of audio-visual aids help in maintaining discipline in the class since all the students' attention are focused in learning. | https://en.wikipedia.org/wiki/Audiovisual_education |
This interactive session also develops critical thinking and reasoning that are important components of the teaching-learning process.Audiovisual provides opportunities for effective communication between teacher and students in learning. For example, in a study on English as Foreign Language (EFL) classroom, the difficulties faced by EFL learner are lack of motivation, lack of exposure to the target language and lack of pronunciation by teacher, and such difficulties can be overcome by Audio as purpose of communication and Visual as more exposure.Students learn when they are motivated and curious about something. Traditional verbal instructions can be boring and painful for students. However, use of audio-visual provides intrinsic motivation to students by peaking their curiosity and stimulating their interests in the subjects. | https://en.wikipedia.org/wiki/Audiovisual_education |
In modern world, digital computers do contribute a lot to higher speed and efficiency in data analysis. Thus, it is necessary to convert an analog signal into a digital signal by sample the signal in time domain. The operation can be realized by three devices: a digital conversion device, a dynamic range controller and a digital conversion device. For simplicity, the sampling is done at equal time intervals. In order to prevent the distortion (that is aliasing in frequency domain) after reconstructing the signal from sampled signal, one must sample at a faster rate.The sampling rate, which can well preserves the information content of an analog signal s ( t , r → ) {\displaystyle s(t,{\vec {r}})} , is submitted to the Nyquist–Shannon sampling theorem. Assuming the sampling period is T, thus after temporal sampling, the signal is r ( t ) = r ( n T ) = s ( r → , n T ) {\displaystyle r(t)=r(nT)=s({\vec {r}},nT)} n is the integer. | https://en.wikipedia.org/wiki/Sonar_signal_processing |
In modern yoga as exercise, the handstand is among the inverted poses; it is known as Adho Mukha Vrksasana, Downward-facing Tree Pose. In traditional hatha yoga in the 18th and 19th centuries, the Vyayāmadipike, which calls it the "second gardam", and the Śrītattvanidhi use the handstand in a sequence involving touching the nose to the ground; the Haṭhābhyāsapaddhati calls this Syenasana, meaning hawk pose. | https://en.wikipedia.org/wiki/Hand_stand |
In modern, digital audio workstation-based recording environments, punching in and out can be done automatically by pre-selecting the in and out points on the timeline of the DAW. When the record button is pressed, the DAW software will play back the previously recorded track outside of these points. As soon as the playhead reaches the in-point, the recording begins and the previously recorded material is muted. At the out-point, recording stops and the software reverts to playback. | https://en.wikipedia.org/wiki/Punch_in/out |
In modern, often mobile, hydraulic systems the preferred item is a gas charged accumulator, but simple systems may be spring-loaded. There may be more than one accumulator in a system. The exact type and placement of each may be a compromise due to its effects and the costs of manufacture. An accumulator is placed close to the pump with a non-return valve preventing flow back to the pump. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
In the case of piston-type pumps this accumulator is placed in the ideal location to absorb pulsations of energy from the multi-piston pump. It also helps protect the system from fluid hammer. This protects system components, particularly pipework, from both potentially destructive forces. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
An additional benefit is the additional energy that can be stored while the pump is subject to low demand. The designer can use a smaller-capacity pump. The large excursions of system components, such as landing gear on a large aircraft, that require a considerable volume of fluid can also benefit from one or more accumulators. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
These are often placed close to the demand to help overcome restrictions and drag from long pipework runs. The outflow of energy from a discharging accumulator is much greater, for a short time, than even large pumps could generate. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
An accumulator can maintain the pressure in a system for periods when there are slight leaks without the pump being cycled on and off constantly. When temperature changes cause pressure excursions the accumulator helps absorb them. Its size helps absorb fluid that might otherwise be locked in a small fixed system with no room for expansion due to valve arrangement. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
The gas precharge in an accumulator is set so that the separating bladder, diaphragm or piston does not reach or strike either end of the operating cylinder. The design precharge normally ensures that the moving parts do not foul the ends or block fluid passages. Poor maintenance of precharge can destroy an operating accumulator. A properly designed and maintained accumulator should operate trouble-free for years. | https://en.wikipedia.org/wiki/Hydraulic_accumulator |
In modern, well-regulated zoos, breeding is controlled to maintain a self-sustaining, global captive population. This is not the case in some less well-regulated zoos, often based in poorer regions. Overall "stock turnover" of animals during a year in a select group of poor zoos was reported as 20%-25% with 75% of wild caught apes dying in captivity within the first 20 months. | https://en.wikipedia.org/wiki/Zoo |
The authors of the report stated that before successful breeding programs, the high mortality rate was the reason for the "massive scale of importations." One 2-year study indicated that of 19,361 mammals that left accredited zoos in the U.S. between 1992 and 1998, 7,420 (38%) went to dealers, auctions, hunting ranches, unaccredited zoos and individuals, and game farms. | https://en.wikipedia.org/wiki/Zoo |
In modern-day 21st century, medicine has evolved to involve past treatments such as leech therapy, as well as advancing wound prevention and the treatment. A large part of wound care is wound treatment. This involves promoting healing, preventing infections, and getting rid of an already existent infection. Deciding on a treatment depends on the type of wound that a person has sustained. | https://en.wikipedia.org/wiki/Wound_treatment |
Varying from infections to burns, wound care is a priority in saving the limb, extremity, or life of a person. In a hospital or medical care setting, more severe wounds like diabetic ulcers, decubitus ulcers, and burns require sterile or clean (depending on the severity of the wound) dressings and wound care. The types of wound dressing include: dry dressings, wet-to-dry dressings, chemical-impregnated dressings, foam dressings, alginate dressings, hydrofiber dressings, transparent film dressings, hydrogel dressings, and hydrocolloid dressings. | https://en.wikipedia.org/wiki/Wound_treatment |
All of the listed dressing types require different materials to complete the dressing. Dry dressings: these dressings are typically composed of a gauze material and used for wounds with a small amount of drainage. These dressings are good for keeping the wound covered after cleaning and to promote healing as well as taking out small amounts of infection. | https://en.wikipedia.org/wiki/Wound_treatment |
Wet-to-dry dressings: Although some medical facilities are stepping away from these types of dressings, they are used mostly for post-surgical wound care as well as debridement of wounds. These dressings take out necrotic areas as well as infections. In this type of wound dressing, gauze is soaked in saline, placed lightly inside of the wound, and covered with a dry dressing. | https://en.wikipedia.org/wiki/Wound_treatment |
Once the gauze dries, it can be removed. It dries onto the infection or necrotic areas to remove them. These dressings are being replaced by Wound-Vacs, which are attached to a dressing directly onto the wound, and lightly but continuously, pull and suck exudate and fluids from the wound. | https://en.wikipedia.org/wiki/Wound_treatment |
Chemical-impregnated dressings: these are provided by manufacturers and they contain chemicals and agents that promote the healing process. Some of these dressings come in sheets and require secondary dressings. Foam dressings: dressings that require additional padding utilize foam pads to help absorb and provide a moist healing environment. | https://en.wikipedia.org/wiki/Wound_treatment |
They also act as a shield to the wound and prevent any damage from friction or pressure. They can be tricky when applying and removing due to the surrounding skin. Alginate dressings: these dressings are composed of calcium, sodium salts and also provide a moist environment for the healing process. | https://en.wikipedia.org/wiki/Wound_treatment |
They are better used with a larger wound such as ulcers or donor sites. Hydro-fiber dressings: these dressings are similar to alginate dressings when it comes to absorbing characteristics, but they do not affect hemostasis. | https://en.wikipedia.org/wiki/Wound_treatment |
They are composed in sheets which contain polymer carboxymethylcellulose and can be cut according to wound size and severity. However, when using these dressings, a secondary dressing is almost always required. | https://en.wikipedia.org/wiki/Wound_treatment |
Transparent film dressings: this specific type of dressing is more like a plastic covering for the wound. It allows oxygen to reach it and help heal but does not absorb any fluids. Transparent film dressings are used primarily on dry wounds. | https://en.wikipedia.org/wiki/Wound_treatment |
Hydrogel dressings: this type of dressing is more directed towards infected areas and those in need of a moist environment to heal properly. It helps promote the body's own natural functions of removing necrotic tissue. It is advised not to be used on dry wounds. | https://en.wikipedia.org/wiki/Wound_treatment |
Hydrocolloid dressings: unlike transparent film dressings, hydrocolloid dressings do not allow oxygen to reach the wound. It is a wet-to-dry technique but is not recommended for infected areas. | https://en.wikipedia.org/wiki/Wound_treatment |
This type of dressing can last up to 7 days with a close eye and must be removed with care. Biologically based dressings: Integra LifeSciences’ artificial skin is placed on a wound where burned or scarred skin has been removed. The two-layer membrane provides scaffolding to regrow a new layer of dermis. | https://en.wikipedia.org/wiki/Wound_treatment |
In modern-day American Sign Language (ASL) the gesture can mean many different things depending on how it is applied. The pinching action of the thumb-and-forefinger frequently represents something small. For example, the sign for "housefly" is made by making the gesture mimic a fly buzzing around. In ASL the gesture can also communicate a selection of some sort: When moved from one side to the other as if picking something up and placing it down, it means "appoint". When the joined thumb and forefinger of the gesture are placed into a hole made by the opposite hand, it means "vote". The sign for "elect" is formed by making the signs for "vote" and "appoint" in succession. | https://en.wikipedia.org/wiki/OK_gesture |
In modern-day Mexico there are examples of images (usually caricatures) in blackface (e.g., Memín Pinguín). Though there is backlash from international communities, Mexican society has not protested to have these images changed to racially sensitive images. On the contrary, in the controversial Memín Pinguín cartoon there has been support publicly and politically, such as from the Mexican Secretary of Foreign Affairs Luis Ernesto Derbez. Currently in Mexico, only 3–4% of the population are composed of Afro-Mexicans (this percentage includes Asian Mexicans). | https://en.wikipedia.org/wiki/Digital_blackface |
In modern-day repair and maintenance of early tube-based consumer electronics devices, a glowing plate will be rarely encountered. As a visible symptom of a destructive failure, checking for an overheated tube is essential to ensure the safe and reliable operation of the equipment undergoing maintenance. Most frequently, a glowing plate overload will be found in rectifiers and output tubes. In particular: Rectifier tubes (5U4, 80, etc.), usually due to shorted capacitors or other substantial short circuits within the device. | https://en.wikipedia.org/wiki/Glowing_plate |
The power supply's output may be easily disconnected from the rest of the circuit in order to determine whether the overload is occurring in the supply or elsewhere. Horizontal and vertical output tubes in television sets (6CD6, 21LU8, etc.), usually due to a shorted coupling capacitor upsetting the bias or the driving oscillator operating well out of its design range. Deflection yokes are sometimes faulty. | https://en.wikipedia.org/wiki/Glowing_plate |
Horizontal output tubes may also be overloaded by a flyback transformer with shorted turns, a defective damper (i.e. 6W4), high voltage rectifier (i.e. 1B3) or high voltage regulator (i.e. 6BK4) tube. Early color television receivers also used a complex dynamic convergence system, which was driven by both the horizontal and vertical output stages. Failure of part of this system could overload either tube, though this author has never seen such a failure in person. Audio output tubes in radios, stereos, public address systems and guitar amplifiers (50C5, 6L6, etc.), usually due to a bad coupling capacitor upsetting the bias or a shorted load.If any tube presents a glowing plate, the equipment should be shut down immediately to avoid further damage. == References == | https://en.wikipedia.org/wiki/Glowing_plate |
In modernist literature, the definition of tragedy has become less precise. The most fundamental change has been the rejection of Aristotle's dictum that true tragedy can only depict those with power and high status. Arthur Miller's essay "Tragedy and the Common Man" (1949) argues that tragedy may also depict ordinary people in domestic surroundings thus defining Domestic tragedies. | https://en.wikipedia.org/wiki/Tragedy |
British playwright Howard Barker has argued strenuously for the rebirth of tragedy in the contemporary theatre, most notably in his volume Arguments for a Theatre. "You emerge from tragedy equipped against lies. After the musical, you're anybody's fool," he insists.Critics such as George Steiner have even been prepared to argue that tragedy may no longer exist in comparison with its former manifestations in classical antiquity. | https://en.wikipedia.org/wiki/Tragedy |
In The Death of Tragedy (1961) George Steiner outlined the characteristics of Greek tragedy and the traditions that developed from that period. In the Foreword (1980) to a new edition of his book Steiner concluded that 'the dramas of Shakespeare are not a renascence of or a humanistic variant of the absolute tragic model. They are, rather, a rejection of this model in the light of tragi-comic and "realistic" criteria.' In part, this feature of Shakespeare's mind is explained by his bent of mind or imagination which was 'so encompassing, so receptive to the plurality of diverse orders of experience.' When compared to the drama of Greek antiquity and French classicism Shakespeare's forms are 'richer but hybrid'.Numerous books and plays continue to be written in the tradition of tragedy to this day examples include Froth on the Daydream, The Road, The Fault in Our Stars, Fat City, Rabbit Hole, Requiem for a Dream, The Handmaid's Tale. | https://en.wikipedia.org/wiki/Tragedy |
In modernity, local entrepreneurs and their mints gained in importance. The era saw the rise of Münzmeister dynasties, with leases that were extended over several generations. Frequently the coins bear symbols engraved by the Münzmeister, often as tiny rosettae, tools, monographs or initials. In the 17th and 18th century, the number of Jewish leaseholders in minting increased, in part because access to other occupations became more restricted. | https://en.wikipedia.org/wiki/Münzmeister |
During the Habsburg era in Austria and Germany, the government began to establish a minting system. Austria created the office of a supreme heritable Münzmeister that provided for a sinecure without a share in profits. In Bohemia too, the supreme office of Münzmeister was held by dukes and noblemen who at the same time supervised all the kingdom's mining facilities. | https://en.wikipedia.org/wiki/Münzmeister |
Besides the Münzmeister, there were other minting officials, such as the master smith, the dye-cutter, and the minter. The Münzwardein (in Latin, wardinus) was tasked with making sure that minting was done properly from the right alloy. He also had to take samples that were presented to the Probationstag (sampling commission) in line with official regulations. The sampling commission was constituted from the royal court or local gentry or their representatives. | https://en.wikipedia.org/wiki/Münzmeister |
In modified gravity, the Einstein field equations do not hold and so these singularities do not necessarily arise. For example, in Infinite Derivative Gravity, it is possible for E a a {\displaystyle {E^{a}}_{a}} to be negative even if the Null Energy Condition holds. | https://en.wikipedia.org/wiki/Singularity_theorems |
In modified policy iteration (van Nunen 1976; Puterman & Shin 1978), step one is performed once, and then step two is repeated several times. Then step one is again performed once and so on. | https://en.wikipedia.org/wiki/Markov_Decision_Process |
In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematician Peter L. Montgomery.Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab using division by N and keeping only the remainder. | https://en.wikipedia.org/wiki/Montgomery_modular_multiplication |
This division requires quotient digit estimation and correction. The Montgomery form, in contrast, depends on a constant R > N which is coprime to N, and the only division necessary in Montgomery multiplication is division by R. The constant R can be chosen so that division by R is easy, significantly improving the speed of the algorithm. In practice, R is always a power of two, since division by powers of two can be implemented by bit shifting. | https://en.wikipedia.org/wiki/Montgomery_modular_multiplication |
The need to convert a and b into Montgomery form and their product out of Montgomery form means that computing a single product by Montgomery multiplication is slower than the conventional or Barrett reduction algorithms. However, when performing many multiplications in a row, as in modular exponentiation, intermediate results can be left in Montgomery form. Then the initial and final conversions become a negligible fraction of the overall computation. Many important cryptosystems such as RSA and Diffie–Hellman key exchange are based on arithmetic operations modulo a large odd number, and for these cryptosystems, computations using Montgomery multiplication with R a power of two are faster than the available alternatives. | https://en.wikipedia.org/wiki/Montgomery_modular_multiplication |
In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett.A naive way of computing c = a mod n {\displaystyle c=a\,{\bmod {\,}}n\,} would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming n {\displaystyle n} is constant, and a < n 2 {\displaystyle a | https://en.wikipedia.org/wiki/Barrett_reduction |
In modular arithmetic, Thue's lemma roughly states that every modular integer may be represented by a "modular fraction" such that the numerator and the denominator have absolute values not greater than the square root of the modulus. More precisely, for every pair of integers (a, m) with m > 1, given two positive integers X and Y such that X ≤ m < XY, there are two integers x and y such that a y ≡ x ( mod m ) {\displaystyle ay\equiv x{\pmod {m}}} and | x | < X , 0 < y < Y . {\displaystyle |x| | https://en.wikipedia.org/wiki/Thue's_lemma |
In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n. Gauss defined primitive roots in Article 57 of the Disquisitiones Arithmeticae (1801), where he credited Euler with coining the term. In Article 56 he stated that Lambert and Euler knew of them, but he was the first to rigorously demonstrate that primitive roots exist for a prime n. In fact, the Disquisitiones contains two proofs: The one in Article 54 is a nonconstructive existence proof, while the proof in Article 55 is constructive. | https://en.wikipedia.org/wiki/Primitive_root_modulo_p |
In modular arithmetic, any unit fraction can be converted into an equivalent whole number using the extended Euclidean algorithm. This conversion can be used to perform modular division: dividing by a number x {\displaystyle x} , modulo y {\displaystyle y} , can be performed by converting the unit fraction 1 / x {\displaystyle 1/x} into an equivalent whole number modulo y {\displaystyle y} , and then multiplying by that number.In more detail, suppose that x {\displaystyle x} is relatively prime to y {\displaystyle y} (otherwise, division by x {\displaystyle x} is not defined modulo y {\displaystyle y} ). The extended Euclidean algorithm for the greatest common divisor can be used to find integers a {\displaystyle a} and b {\displaystyle b} such that Bézout's identity is satisfied: In modulo- y {\displaystyle y} arithmetic, the term b y {\displaystyle by} can be eliminated as it is zero modulo y {\displaystyle y} . This leaves That is, a {\displaystyle a} is the modular inverse of x {\displaystyle x} , the number that when multiplied by x {\displaystyle x} produces one. Equivalently, Thus division by x {\displaystyle x} (modulo y {\displaystyle y} ) can instead be performed by multiplying by the integer a {\displaystyle a} . | https://en.wikipedia.org/wiki/Unit_fractions |
In modular arithmetic, the integers coprime (relatively prime) to n from the set { 0 , 1 , … , n − 1 } {\displaystyle \{0,1,\dots ,n-1\}} of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which, in this ring, are exactly those coprime to n. This quotient group, usually denoted ( Z / n Z ) × {\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{\times }} , is fundamental in number theory. It is used in cryptography, integer factorization, and primality testing. It is an abelian, finite group whose order is given by Euler's totient function: | ( Z / n Z ) × | = φ ( n ) . {\displaystyle |(\mathbb {Z} /n\mathbb {Z} )^{\times }|=\varphi (n).} For prime n the group is cyclic, and in general the structure is easy to describe, but no simple general formula for finding generators is known. | https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n |
In modular arithmetic, the method of successive substitution is a method of solving problems of simultaneous congruences by using the definition of the congruence equation. It is commonly applied in cases where the conditions of the Chinese remainder theorem are not satisfied. There is also an unrelated numerical-analysis method of successive substitution, a randomized algorithm used for root finding, an application of fixed-point iteration. The method of successive substitution is also known as back substitution. | https://en.wikipedia.org/wiki/Method_of_successive_substitution |
In modular arithmetic, the set of available numbers is restricted to a finite subset of the integers, and addition "wraps around" when reaching a certain value, called the modulus. For example, the set of integers modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2 has just two elements; the addition operation it inherits is known in Boolean logic as the "exclusive or" function. A similar "wrap around" operation arises in geometry, where the sum of two angle measures is often taken to be their sum as real numbers modulo 2π. This amounts to an addition operation on the circle, which in turn generalizes to addition operations on many-dimensional tori. | https://en.wikipedia.org/wiki/Addition |
In modular construction, modules are a bundle of redundant project components that are produced en masse prior to installation.Building components are often arranged into modules in the industrialization of construction. In industrial design, modularity refers to an engineering technique that builds larger systems by combining smaller subsystems. In manufacturing, modularity typically refers to modular design, either as the use of exchangeable parts or options in the fabrication of an object or the design and manufacture of modular components. In organizational design, Richard L. Daft and Arie Y. Lewin (1993) identified a paradigm called "modular organization" that had as its ground the need for flexible learning organizations in constant change and the need to solve their problems through coordinated self-organizing processes. This modular organization is characterized by decentralized decision-making, flatter hierarchies, self-organization of units. | https://en.wikipedia.org/wiki/Modularity |
In modular programming, modularity refers to the compartmentalization and interrelation of the parts of a software package. In software design, modularity refers to a logical partitioning of the "software design" that allows complex software to be manageable for the purpose of implementation and maintenance. The logic of partitioning may be based on related functions, implementation considerations, data links, or other criteria. In self-reconfiguring modular robotics, modularity refers to the ability of the robotic system to automatically achieve different morphologies to execute the task at hand. | https://en.wikipedia.org/wiki/Modularity |
In modular representation theory, and more generally in the theory of representations of finite-dimensional associative algebras A that are not semisimple, a Cartan matrix is defined by considering a (finite) set of principal indecomposable modules and writing composition series for them in terms of irreducible modules, yielding a matrix of integers counting the number of occurrences of an irreducible module. | https://en.wikipedia.org/wiki/Cartan_matrices |
In modular representation theory, while Maschke's theorem does not hold when the characteristic divides the group order, the group algebra may be decomposed as the direct sum of a maximal collection of two-sided ideals known as blocks. When the field F has characteristic 0, or characteristic coprime to the group order, there is still such a decomposition of the group algebra F as a sum of blocks (one for each isomorphism type of simple module), but the situation is relatively transparent when F is sufficiently large: each block is a full matrix algebra over F, the endomorphism ring of the vector space underlying the associated simple module. To obtain the blocks, the identity element of the group G is decomposed as a sum of primitive idempotents in Z(R), the center of the group algebra over the maximal order R of F. The block corresponding to the primitive idempotent e is the two-sided ideal e R. For each indecomposable R-module, there is only one such primitive idempotent that does not annihilate it, and the module is said to belong to (or to be in) the corresponding block (in which case, all its composition factors also belong to that block). In particular, each simple module belongs to a unique block. Each ordinary irreducible character may also be assigned to a unique block according to its decomposition as a sum of irreducible Brauer characters. The block containing the trivial module is known as the principal block. | https://en.wikipedia.org/wiki/Modular_representation |
In module Data.Ratio (1 % 10) + (2 % 10) ⇒ 3 % 10 | https://en.wikipedia.org/wiki/Rational_data_type |
In modulus 12, one can assert that: 38 ≡ 14 ( mod 12 ) {\displaystyle 38\equiv 14{\pmod {12}}} because 38 − 14 = 24, which is a multiple of 12. Another way to express this is to say that both 38 and 14 have the same remainder 2, when divided by 12. The definition of congruence also applies to negative values. For example: 2 ≡ − 3 ( mod 5 ) − 8 ≡ 7 ( mod 5 ) − 3 ≡ − 8 ( mod 5 ) . {\displaystyle {\begin{aligned}2&\equiv -3{\pmod {5}}\\-8&\equiv 7{\pmod {5}}\\-3&\equiv -8{\pmod {5}}.\end{aligned}}} | https://en.wikipedia.org/wiki/Modular_arithmatic |
In molding, an undercut is an indentation or protrusion in a shape that will prevent its withdrawal from a one-piece mold. Undercuts on molded parts are features that prevent the part from being directly ejected from an injection molding machine. They are categorized into internal and external undercuts, where external undercuts are on the exterior of the part and interior undercuts are on the inside of the part. Undercuts can still be molded, but require a side action or side pull. | https://en.wikipedia.org/wiki/Undercut_(molding) |
This is an extra part of the mold that moves separately from the two halves. These can increase the cost of the molded part due to an added 15 to 30% cost of the mold itself and added complexity of the molding machine.If the size of the undercut is small enough and the material is flexible enough a side action is not always required. In these cases the undercut is stripped or snapped out of the mold. When this is done usually a stripping plate or ring is used instead of ejector pins so that the part is not damaged. This technique can be used on internal and external undercuts. | https://en.wikipedia.org/wiki/Undercut_(molding) |
In molecular beam epitaxy (MBE) heated gaseous elements are allowed to condense on the wafer. MBE has been used to grow h-BN films from elemental B and N on Ni foils.Molten boron oxide reacts with gaseous ammonia to form an ultrathin h-BN film at the reaction interface. The film grows to 20-30 nm in thickness, after which the process self-terminates, the setup is cooled down, and the boron oxide can be dissolved in water. == References == | https://en.wikipedia.org/wiki/Synthesis_of_hexagonal_boron_nitride |
In molecular biology (specifically protein biosynthesis), a stop codon (or termination codon) is a codon (nucleotide triplet within messenger RNA) that signals the termination of the translation process of the current protein. Most codons in messenger RNA correspond to the addition of an amino acid to a growing polypeptide chain, which may ultimately become a protein; stop codons signal the termination of this process by binding release factors, which cause the ribosomal subunits to disassociate, releasing the amino acid chain. While start codons need nearby sequences or initiation factors to start translation, a stop codon alone is sufficient to initiate termination. | https://en.wikipedia.org/wiki/Stop_codon |
In molecular biology 2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline decarboxylase (OHCU decarboxylase) EC 4.1.1.n1 is an enzyme involved in purine catabolism. It catalyses the decarboxylation of 2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline (OHCU) into S(+)-allantoin. It is the third step of the conversion of uric acid (a purine derivative) to allantoin. Step one is catalysed by urate oxidase and step two is catalysed by hydroxyisourate hydrolase. == References == | https://en.wikipedia.org/wiki/2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline_decarboxylase |
In molecular biology 7SK is an abundant small nuclear RNA found in metazoans. It plays a role in regulating transcription by controlling the positive transcription elongation factor P-TEFb. 7SK is found in a small nuclear ribonucleoprotein complex (snRNP) with a number of other proteins that regulate the stability and function of the complex. | https://en.wikipedia.org/wiki/7SK_RNA |
In molecular biology FAD-oxidases are a family of FAD-dependent oxidoreductases. They are flavoproteins that contain a covalently bound FAD group which is attached to a histidine via an 8-alpha-(N3-histidyl)-riboflavin linkage. The region around the histidine that binds the FAD group is conserved in these enzymes. == References == | https://en.wikipedia.org/wiki/FAD-oxidase |
In molecular biology Type I topoisomerases are enzymes that cut one of the two strands of double-stranded DNA, relax the strand, and reanneal the strand. They are further subdivided into two structurally and mechanistically distinct topoisomerases: type IA and type IB. Type IA topoisomerases change the linking number of a circular DNA strand by units of strictly 1. Type IB topoisomerases change the linking number by multiples of 1 (n).Historically, type IA topoisomerases are referred to as prokaryotic topo I, while type IB topoisomerases are referred to as eukaryotic topoisomerase. | https://en.wikipedia.org/wiki/Type_I_topoisomerase |
This distinction, however, no longer applies as type IA and type IB topoisomerases exist in all domains of life. Functionally, these subclasses perform very specialized functions. Prokaryotic topoisomerase I (topo IA) can only relax negative supercoiled DNA, whereas eukaryotic topoisomerase I (topo IB) can introduce positive supercoils, separating the DNA of daughter chromosomes after DNA replication, and relax DNA. | https://en.wikipedia.org/wiki/Type_I_topoisomerase |
In molecular biology and biochemistry, processivity is an enzyme's ability to catalyze "consecutive reactions without releasing its substrate".For example, processivity is the average number of nucleotides added by a polymerase enzyme, such as DNA polymerase, per association event with the template strand. Because the binding of the polymerase to the template is the rate-limiting step in DNA synthesis, the overall rate of DNA replication during S phase of the cell cycle is dependent on the processivity of the DNA polymerases performing the replication. DNA clamp proteins are integral components of the DNA replication machinery and serve to increase the processivity of their associated polymerases. Some polymerases add over 50,000 nucleotides to a growing DNA strand before dissociating from the template strand, giving a replication rate of up to 1,000 nucleotides per second. | https://en.wikipedia.org/wiki/Processivity |
In molecular biology and bioinformatics, the consensus sequence (or canonical sequence) is the calculated sequence of most frequent residues, either nucleotide or amino acid, found at each position in a sequence alignment. It represents the results of multiple sequence alignments in which related sequences are compared to each other and similar sequence motifs are calculated. Such information is important when considering sequence-dependent enzymes such as RNA polymerase. | https://en.wikipedia.org/wiki/Canonical_sequence |
In molecular biology and biotechnology, a fluorescent tag, also known as a fluorescent label or fluorescent probe, is a molecule that is attached chemically to aid in the detection of a biomolecule such as a protein, antibody, or amino acid. Generally, fluorescent tagging, or labeling, uses a reactive derivative of a fluorescent molecule known as a fluorophore. The fluorophore selectively binds to a specific region or functional group on the target molecule and can be attached chemically or biologically. | https://en.wikipedia.org/wiki/Fluorescent_labelling |
Various labeling techniques such as enzymatic labeling, protein labeling, and genetic labeling are widely utilized. Ethidium bromide, fluorescein and green fluorescent protein are common tags. The most commonly labelled molecules are antibodies, proteins, amino acids and peptides which are then used as specific probes for detection of a particular target. | https://en.wikipedia.org/wiki/Fluorescent_labelling |
In molecular biology and genetics, DNA annotation or genome annotation is the process of describing the structure and function of the components of a genome, by analyzing and interpreting them in order to extract their biological significance and understand the biological processes in which they participate. Among other things, it identifies the locations of genes and all the coding regions in a genome and determines what those genes do.Annotation is performed after a genome is sequenced and assembled, and is a necessary step in genome analysis before the sequence is deposited in a database and described in a published article. Although describing individual genes and their products or functions is sufficient to consider this description as an annotation, the depth of analysis reported in literature for different genomes vary widely, with some reports including additional information that goes beyond a simple annotation. | https://en.wikipedia.org/wiki/Genome_annotation |
Furthermore, due to the size and complexity of sequenced genomes, DNA annotation is not performed manually, but is instead automated by computational means. However, the conclusions drawn from the obtained results require manual expert analysis.DNA annotation is classified into two categories: structural annotation, which identifies and demarcates elements in a genome, and functional annotation, which assigns functions to these elements. This is not the only way in which it has been categorized, as several alternatives, such as dimension-based and level-based classifications, have also been proposed. | https://en.wikipedia.org/wiki/Genome_annotation |
In molecular biology and genetics, GC-content (or guanine-cytosine content) is the percentage of nitrogenous bases in a DNA or RNA molecule that are either guanine (G) or cytosine (C). This measure indicates the proportion of G and C bases out of an implied four total bases, also including adenine and thymine in DNA and adenine and uracil in RNA. GC-content may be given for a certain fragment of DNA or RNA or for an entire genome. When it refers to a fragment, it may denote the GC-content of an individual gene or section of a gene (domain), a group of genes or gene clusters, a non-coding region, or a synthetic oligonucleotide such as a primer. | https://en.wikipedia.org/wiki/Guanine-cytosine_content |
In molecular biology and genetics, the sense of a nucleic acid molecule, particularly of a strand of DNA or RNA, refers to the nature of the roles of the strand and its complement in specifying a sequence of amino acids. Depending on the context, sense may have slightly different meanings. For example, negative-sense strand of DNA is equivalent to the template strand, whereas the positive-sense strand is the non-template strand whose nucleotide sequence is equivalent to the sequence of the mRNA transcript. | https://en.wikipedia.org/wiki/Non-coding_strand |
In molecular biology and genetics, transcription coregulators are proteins that interact with transcription factors to either activate or repress the transcription of specific genes. Transcription coregulators that activate gene transcription are referred to as coactivators while those that repress are known as corepressors. The mechanism of action of transcription coregulators is to modify chromatin structure and thereby make the associated DNA more or less accessible to transcription. | https://en.wikipedia.org/wiki/Transcription_coregulator |
In humans several dozen to several hundred coregulators are known, depending on the level of confidence with which the characterisation of a protein as a coregulator can be made. One class of transcription coregulators modifies chromatin structure through covalent modification of histones. A second ATP dependent class modifies the conformation of chromatin. | https://en.wikipedia.org/wiki/Transcription_coregulator |
In molecular biology and genetics, transcriptional regulation is the means by which a cell regulates the conversion of DNA to RNA (transcription), thereby orchestrating gene activity. A single gene can be regulated in a range of ways, from altering the number of copies of RNA that are transcribed, to the temporal control of when the gene is transcribed. This control allows the cell or organism to respond to a variety of intra- and extracellular signals and thus mount a response. Some examples of this include producing the mRNA that encode enzymes to adapt to a change in a food source, producing the gene products involved in cell cycle specific activities, and producing the gene products responsible for cellular differentiation in multicellular eukaryotes, as studied in evolutionary developmental biology. | https://en.wikipedia.org/wiki/Transcriptional_regulator |
The regulation of transcription is a vital process in all living organisms. It is orchestrated by transcription factors and other proteins working in concert to finely tune the amount of RNA being produced through a variety of mechanisms. Bacteria and eukaryotes have very different strategies of accomplishing control over transcription, but some important features remain conserved between the two. Most importantly is the idea of combinatorial control, which is that any given gene is likely controlled by a specific combination of factors to control transcription. In a hypothetical example, the factors A and B might regulate a distinct set of genes from the combination of factors A and C. This combinatorial nature extends to complexes of far more than two proteins, and allows a very small subset (less than 10%) of the genome to control the transcriptional program of the entire cell. | https://en.wikipedia.org/wiki/Transcriptional_regulator |
In molecular biology and genetics, transformation is the genetic alteration of a cell resulting from the direct uptake and incorporation of exogenous genetic material from its surroundings through the cell membrane(s). For transformation to take place, the recipient bacterium must be in a state of competence, which might occur in nature as a time-limited response to environmental conditions such as starvation and cell density, and may also be induced in a laboratory.Transformation is one of three processes that lead to horizontal gene transfer, in which exogenous genetic material passes from one bacterium to another, the other two being conjugation (transfer of genetic material between two bacterial cells in direct contact) and transduction (injection of foreign DNA by a bacteriophage virus into the host bacterium). In transformation, the genetic material passes through the intervening medium, and uptake is completely dependent on the recipient bacterium.As of 2014 about 80 species of bacteria were known to be capable of transformation, about evenly divided between Gram-positive and Gram-negative bacteria; the number might be an overestimate since several of the reports are supported by single papers. "Transformation" may also be used to describe the insertion of new genetic material into nonbacterial cells, including animal and plant cells; however, because "transformation" has a special meaning in relation to animal cells, indicating progression to a cancerous state, the process is usually called "transfection". | https://en.wikipedia.org/wiki/Genetic_transformation |
In molecular biology and genetics, upstream and downstream both refer to relative positions of genetic code in DNA or RNA. Each strand of DNA or RNA has a 5' end and a 3' end, so named for the carbon position on the deoxyribose (or ribose) ring. By convention, upstream and downstream relate to the 5' to 3' direction respectively in which RNA transcription takes place. Upstream is toward the 5' end of the RNA molecule and downstream is toward the 3' end. | https://en.wikipedia.org/wiki/Upstream_and_downstream_(DNA) |
When considering double-stranded DNA, upstream is toward the 5' end of the coding strand for the gene in question and downstream is toward the 3' end. Due to the anti-parallel nature of DNA, this means the 3' end of the template strand is upstream of the gene and the 5' end is downstream. | https://en.wikipedia.org/wiki/Upstream_and_downstream_(DNA) |
Some genes on the same DNA molecule may be transcribed in opposite directions. This means the upstream and downstream areas of the molecule may change depending on which gene is used as the reference. The terms upstream and downstream are sometimes also applied to a polypeptide sequence, where upstream refers to a region N-terminal and downstream to residues C-terminal of a reference point. | https://en.wikipedia.org/wiki/Upstream_and_downstream_(DNA) |
In molecular biology and pharmacology, a small molecule or micromolecule is a low molecular weight (≤ 1000 daltons) organic compound that may regulate a biological process, with a size on the order of 1 nm. Many drugs are small molecules; the terms are equivalent in the literature. Larger structures such as nucleic acids and proteins, and many polysaccharides are not small molecules, although their constituent monomers (ribo- or deoxyribonucleotides, amino acids, and monosaccharides, respectively) are often considered small molecules. Small molecules may be used as research tools to probe biological function as well as leads in the development of new therapeutic agents. | https://en.wikipedia.org/wiki/Small_molecules |
Some can inhibit a specific function of a protein or disrupt protein–protein interactions.Pharmacology usually restricts the term "small molecule" to molecules that bind specific biological macromolecules and act as an effector, altering the activity or function of the target. Small molecules can have a variety of biological functions or applications, serving as cell signaling molecules, drugs in medicine, pesticides in farming, and in many other roles. These compounds can be natural (such as secondary metabolites) or artificial (such as antiviral drugs); they may have a beneficial effect against a disease (such as drugs) or may be detrimental (such as teratogens and carcinogens). | https://en.wikipedia.org/wiki/Small_molecules |
In molecular biology and physiology, something is GABAergic or GABAnergic if it pertains to or affects the neurotransmitter gamma-aminobutyric acid (GABA). For example, a synapse is GABAergic if it uses GABA as its neurotransmitter, and a GABAergic neuron produces GABA. A substance is GABAergic if it produces its effects via interactions with the GABA system, such as by stimulating or blocking neurotransmission. A GABAergic or GABAnergic agent is any chemical that modifies the effects of GABA in the body or brain. Some different classes of GABAergic drugs include agonists, antagonists, modulators, reuptake inhibitors and enzymes. | https://en.wikipedia.org/wiki/GABAergic |
In molecular biology ctRNA (counter-transcribed RNA) is a plasmid encoded noncoding RNA that binds to the mRNA of repB and causes translational inhibition. ctRNA is encoded by plasmids and functions in rolling circle replication to maintain a low copy number. In Corynebacterium glutamicum, it achieves this by antisense pairing with the mRNA of RepB, a replication initiation protein. In Enterococcus faecium the plasmid pJB01 contains three open reading frames, copA, repB, and repC. The pJB01 ctRNA is coded on the opposite strand from the copA/repB intergenic region and partially overlaps an atypical ribosome binding site for repB. | https://en.wikipedia.org/wiki/CtRNA |
In molecular biology lin-4 is a microRNA (miRNA) that was identified from a study of developmental timing in the nematode Caenorhabditis elegans. It was the first to be discovered of the miRNAs, a class of non-coding RNAs involved in gene regulation. miRNAs are transcribed as ~70 nucleotide precursors and subsequently processed by the Dicer enzyme to give a 21 nucleotide product. The extents of the hairpin precursors are not generally known and are estimated based on hairpin prediction. The products are thought to have regulatory roles through complete or partial complementarity to mRNA. The lin-4 gene has been found to lie within a 4.11kb intron of a separate host gene (see also ). | https://en.wikipedia.org/wiki/Lin-4_microRNA_precursor |
In molecular biology miR-132 microRNA is a short non-coding RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms, generally reducing protein levels through the cleavage of mRNAs or the repression of their translation. Several targets for miR-132 have been described, including mediators of neurological development, synaptic transmission, inflammation and angiogenesis. | https://en.wikipedia.org/wiki/Mir-132_microRNA |
In molecular biology miR-181 microRNA precursor is a small non-coding RNA molecule. MicroRNAs (miRNAs) are transcribed as ~70 nucleotide precursors and subsequently processed by the RNase-III type enzyme Dicer to give a ~22 nucleotide mature product. In this case the mature sequence comes from the 5' arm of the precursor. They target and modulate protein expression by inhibiting translation and / or inducing degradation of target messenger RNAs. | https://en.wikipedia.org/wiki/Mir-181_microRNA_precursor |
This new class of genes has recently been shown to play a central role in malignant transformation. miRNA are downregulated in many tumors and thus appear to function as tumor suppressor genes. The mature products miR-181a, miR-181b, miR-181c or miR-181d are thought to have regulatory roles at posttranscriptional level, through complementarity to target mRNAs. miR-181 which has been predicted or experimentally confirmed in a wide number of vertebrate species as rat, zebrafish, and in the pufferfish (see below) (MIPF0000007). | https://en.wikipedia.org/wiki/Mir-181_microRNA_precursor |
In molecular biology mir-11 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. There is an evidence to suggest that miR-11 plays a role in apoptosis.Alignment has shown that miR-11 shares the same family motif as miR-2b and miR-6, together making up the mir-2 clan. There is however little similarity in the 3' ends between these clan members. | https://en.wikipedia.org/wiki/Mir-11_microRNA_precursor_family |
In molecular biology mir-14 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. | https://en.wikipedia.org/wiki/Mir-14_microRNA_precursor_family |
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