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There are, however, some potential drawbacks to using stratified sampling. First, identifying strata and implementing such an approach can increase the cost and complexity of sample selection, as well as leading to increased complexity of population estimates. Second, when examining multiple criteria, stratifying varia... | Sampling (statistics) | Wikipedia | 425 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
Oversampling
Choice-based sampling or oversampling is one of the stratified sampling strategies. In choice-based sampling, the data are stratified on the target and a sample is taken from each stratum so that rarer target classes will be more represented in the sample. The model is then built on this biased sample. The... | Sampling (statistics) | Wikipedia | 369 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
Example: Suppose we have six schools with populations of 150, 180, 200, 220, 260, and 490 students respectively (total 1500 students), and we want to use student population as the basis for a PPS sample of size three. To do this, we could allocate the first school numbers 1 to 150, the second school 151 to 330 (= 150 +... | Sampling (statistics) | Wikipedia | 494 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
Cluster sampling (also known as clustered sampling) generally increases the variability of sample estimates above that of simple random sampling, depending on how the clusters differ between one another as compared to the within-cluster variation. For this reason, cluster sampling requires a larger sample than SRS to a... | Sampling (statistics) | Wikipedia | 448 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
In imbalanced datasets, where the sampling ratio does not follow the population statistics, one can resample the dataset in a conservative manner called minimax sampling. The minimax sampling has its origin in Anderson minimax ratio whose value is proved to be 0.5: in a binary classification, the class-sample sizes sho... | Sampling (statistics) | Wikipedia | 460 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
In social science research, snowball sampling is a similar technique, where existing study subjects are used to recruit more subjects into the sample. Some variants of snowball sampling, such as respondent driven sampling, allow calculation of selection probabilities and are probability sampling methods under certain c... | Sampling (statistics) | Wikipedia | 477 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
Theoretical sampling occurs when samples are selected on the basis of the results of the data collected so far with a goal of developing a deeper understanding of the area or develop theories. An initial, general sample is first collected with the goal of investigating general trends, where further sampling may consist... | Sampling (statistics) | Wikipedia | 464 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
Applications of sampling
Sampling enables the selection of right data points from within the larger data set to estimate the characteristics of the whole population. For example, there are about 600 million tweets produced every day. It is not necessary to look at all of them to determine the topics that are discussed ... | Sampling (statistics) | Wikipedia | 451 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
In survey sampling, many of the individuals identified as part of the sample may be unwilling to participate, not have the time to participate (opportunity cost), or survey administrators may not have been able to contact them. In this case, there is a risk of differences between respondents and nonrespondents, leading... | Sampling (statistics) | Wikipedia | 454 | 160361 | https://en.wikipedia.org/wiki/Sampling%20%28statistics%29 | Mathematics | Statistics and probability | null | vital_articles |
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them).
These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher d... | Ball (mathematics) | Wikipedia | 504 | 160556 | https://en.wikipedia.org/wiki/Ball%20%28mathematics%29 | Mathematics | Measurement | null | vital_articles |
In particular, a ball (open or closed) always includes itself, since the definition requires . A unit ball (open or closed) is a ball of radius 1.
A ball in a general metric space need not be round. For example, a ball in real coordinate space under the Chebyshev distance is a hypercube, and a ball under the taxicab ... | Ball (mathematics) | Wikipedia | 498 | 160556 | https://en.wikipedia.org/wiki/Ball%20%28mathematics%29 | Mathematics | Measurement | null | vital_articles |
For , the - balls are within octahedra with axes-aligned body diagonals, the -balls are within cubes with axes-aligned edges, and the boundaries of balls for with are superellipsoids. generates the inner of usual spheres.
Often can also consider the case of in which case we define
General convex norm
More general... | Ball (mathematics) | Wikipedia | 392 | 160556 | https://en.wikipedia.org/wiki/Ball%20%28mathematics%29 | Mathematics | Measurement | null | vital_articles |
An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle is supported. ... | Axle | Wikipedia | 485 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
In other types of suspension systems, the axles serve only to transmit driving torque to the wheels: the position and angle of the wheel hubs is made independent from the axles by the function of the suspension system. This is typical of the independent suspensions found on most newer cars, and even SUVs, and on the fr... | Axle | Wikipedia | 467 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
Axles are typically made from SAE grade 41xx steel or SAE grade 10xx steel. SAE grade 41xx steel is commonly known as "chrome-molybdenum steel" (or "chrome-moly") while SAE grade 10xx steel is known as "carbon steel". The primary differences between the two are that chrome-moly steel is significantly more resistant t... | Axle | Wikipedia | 432 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
Some dump trucks and trailers may be configured with a lift axle (also known as an airlift axle or drop axle), which may be mechanically raised or lowered. The axle is lowered to increase the weight capacity, or to distribute the weight of the cargo over more wheels, for example, to cross a weight-restricted bridge. ... | Axle | Wikipedia | 396 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
In contrast, a semi-floating design carries the weight of the vehicle on the axle shaft itself; there is a single bearing at the end of the axle housing that carries the load from the axle and that the axle rotates through. To be "semi-floating" the axle shafts must be able to "float" in the housing, bearings and seals... | Axle | Wikipedia | 512 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
A benefit of a full-floating axle is that even if an axle shaft (used to transmit torque or power) breaks, the wheel will not come off, preventing serious accidents. | Axle | Wikipedia | 36 | 160573 | https://en.wikipedia.org/wiki/Axle | Technology | Components_2 | null | vital_articles |
Tachycardia, also called tachyarrhythmia, is a heart rate that exceeds the normal resting rate. In general, a resting heart rate over 100 beats per minute is accepted as tachycardia in adults. Heart rates above the resting rate may be normal (such as with exercise) or abnormal (such as with electrical problems within t... | Tachycardia | Wikipedia | 404 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
Diagnosis
The upper threshold of a normal human resting heart rate is based on age. Cutoff values for tachycardia in different age groups are fairly well standardized; typical cutoffs are listed below:
1–2 days: Tachycardia >159 beats per minute (bpm)
3–6 days: Tachycardia >166 bpm
1–3 weeks: Tachycardia >182 bpm
1... | Tachycardia | Wikipedia | 274 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
An electrocardiogram (ECG) is used to classify the type of tachycardia. They may be classified into narrow and wide complex based on the QRS complex. Equal or less than 0.1s for narrow complex. Presented in order of most to least common, they are:
Narrow complex
Sinus tachycardia, which originates from the sino-atria... | Tachycardia | Wikipedia | 491 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
Upon exertion, sinus tachycardia can also be seen in some inborn errors of metabolism that result in metabolic myopathies, such as McArdle's disease (GSD-V). Metabolic myopathies interfere with the muscle's ability to create energy. This energy shortage in muscle cells causes an inappropriate rapid heart rate in respon... | Tachycardia | Wikipedia | 468 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
Inappropriate sinus tachycardia (IST) is a diagnosis of exclusion, a rare but benign type of cardiac arrhythmia that may be caused by a structural abnormality in the sinus node. It can occur in seemingly healthy individuals with no history of cardiovascular disease. Other causes may include autonomic nervous system de... | Tachycardia | Wikipedia | 486 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
AV nodal reentrant tachycardia
AV nodal reentrant tachycardia (AVNRT) is the most common reentrant tachycardia. It is a regular narrow complex tachycardia that usually responds well to the Valsalva maneuver or the drug adenosine. However, unstable patients sometimes require synchronized cardioversion. Definitive care m... | Tachycardia | Wikipedia | 449 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
Stable
If the problem is a simple acceleration of the heart rate that worries the patient, but the heart and the general patient's health remain stable enough, it is possible to correct it by a simple deceleration using some physical maneuvers called vagal maneuvers. But, if the cause of the tachycardia is chronic (pe... | Tachycardia | Wikipedia | 137 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
The word tachycardia came to English from Neo-Latin as a neoclassical compound built from the combining forms tachy- + -cardia, which are from the Greek ταχύς tachys, "quick, rapid" and καρδία, kardia, "heart". As a matter both of usage choices in the medical literature and of idiom in natural language, the words tach... | Tachycardia | Wikipedia | 483 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
But the power to differentiate in an idiomatic way is not lost, regardless, because when the specification of physiologic tachycardia is needed, that phrase aptly conveys it | Tachycardia | Wikipedia | 41 | 160581 | https://en.wikipedia.org/wiki/Tachycardia | Biology and health sciences | Symptoms and signs | Health | vital_articles |
Plovers ( , ) are members of a widely distributed group of wading birds of subfamily Charadriinae. The term "plover" applies to all the members of the subfamily, though only about half of them include it in their name.
Species list in taxonomic sequence
The taxonomy of family Charadriidae is unsettled. At various ti... | Plover | Wikipedia | 427 | 160710 | https://en.wikipedia.org/wiki/Plover | Biology and health sciences | Charadriiformes | Animals | vital_articles |
A tunnel is an underground or undersea passageway. It is dug through surrounding soil, earth or rock, or laid under water, and is usually completely enclosed except for the two portals common at each end, though there may be access and ventilation openings at various points along the length. A pipeline differs signific... | Tunnel | Wikipedia | 450 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
In the Mahabharata, the Pandavas built a secret tunnel within their new home, called "Lakshagriha" (House of Lac), which was constructed by Purochana under the orders of Duryodhana by the intention of burning them alive inside, allowing them to escape when the palace was set on fire; this act of foresight by the Pandav... | Tunnel | Wikipedia | 479 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Conventional desk and preliminary site studies may yield insufficient information to assess such factors as the blocky nature of rocks, the exact location of fault zones, or the stand-up times of softer ground. This may be a particular concern in large-diameter tunnels. To give more information, a pilot tunnel (or "dri... | Tunnel | Wikipedia | 460 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Bridges usually require a larger footprint on each shore than tunnels. In areas with expensive real estate, such as Manhattan and urban Hong Kong, this is a strong factor in favor of a tunnel. Boston's Big Dig project replaced elevated roadways with a tunnel system to increase traffic capacity, hide traffic, reclaim la... | Tunnel | Wikipedia | 433 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
There are particular hazards with tunnels, especially from vehicle fires when combustion gases can asphyxiate users, as happened at the Gotthard Road Tunnel in Switzerland in 2001. One of the worst railway disasters ever, the Balvano train disaster, was caused by a train stalling in the Armi tunnel in Italy in 1944, ki... | Tunnel | Wikipedia | 495 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
There are two basic forms of cut-and-cover tunnelling:
Bottom-up method: A trench is excavated, with ground support as necessary, and the tunnel is constructed in it. The tunnel may be of in situ concrete, precast concrete, precast arches, or corrugated steel arches; in early days brickwork was used. The trench is the... | Tunnel | Wikipedia | 439 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Prior to the replacement of manual excavation by the use of boring machines, Victorian tunnel excavators developed a specialized method called clay-kicking for digging tunnels in clay-based soils. The clay-kicker lies on a plank at a 45-degree angle away from the working face and rather than a mattock with his hands, i... | Tunnel | Wikipedia | 320 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
There are a variety of TBM designs that can operate in a variety of conditions, from hard rock to soft water-bearing ground. Some TBMs, the bentonite slurry and earth-pressure balance types, have pressurized compartments at the front end, allowing them to be used in difficult conditions below the water table. This pres... | Tunnel | Wikipedia | 404 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
A temporary access shaft is sometimes necessary during the excavation of a tunnel. They are usually circular and go straight down until they reach the level at which the tunnel is going to be built. A shaft normally has concrete walls and is usually built to be permanent. Once the access shafts are complete, TBMs are l... | Tunnel | Wikipedia | 421 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Box jacking
Box jacking is similar to pipe jacking, but instead of jacking tubes, a box-shaped tunnel is used. Jacked boxes can be a much larger span than a pipe jack, with the span of some box jacks in excess of . A cutting head is normally used at the front of the box being jacked, and spoil removal is normally by e... | Tunnel | Wikipedia | 506 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Drilling and blasting
Hydraulic splitter
Slurry-shield machine
Wall-cover construction method.
Variant tunnel types
Double-deck and multipurpose tunnels
Some tunnels are double-deck, for example, the two major segments of the San Francisco–Oakland Bay Bridge (completed in 1936) are linked by a double-deck tunne... | Tunnel | Wikipedia | 463 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The Alaskan Way Viaduct replacement tunnel, is a $3.3 billion , double-decker bored highway tunnel under Downtown Seattle. Construction began in July 2013 using "Bertha", at the time the world's largest earth pressure balance tunnel boring machine, with a cutterhead diameter. After several delays, tunnel boring was co... | Tunnel | Wikipedia | 369 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Mount Baker Tunnel has three levels. The bottom level is to be used by Sound Transit light rail. The middle level is used by car traffic, and the top layer is for bicycle and pedestrian access.
Some tunnels have more than one purpose. The SMART Tunnel in Malaysia is the first multipurpose "Stormwater Management And R... | Tunnel | Wikipedia | 398 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Owing to the enclosed space of a tunnel, fires can have very serious effects on users. The main dangers are gas and smoke production, with even low concentrations of carbon monoxide being highly toxic. Fires killed 11 people in the Gotthard tunnel fire of 2001 for example, all of the victims succumbing to smoke and gas... | Tunnel | Wikipedia | 485 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Underground structures suffer appreciably less damage than surface structures.
Reported damage decreases with increasing over burden depth. Deep tunnels seem to be safer and less vulnerable to earthquake shaking than are shallow tunnels.
Underground facilities constructed in soils can be expected to suffer more damag... | Tunnel | Wikipedia | 464 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
This same trend of limited subway damage following an earthquake can be seen in many other places. In 1985 a magnitude 8.1 earthquake shook Mexico City; there was no damage to the subway system, and in fact the subway systems served as a lifeline for emergency personnel and evacuations. A magnitude 7.2 ripped through K... | Tunnel | Wikipedia | 199 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The qanat or kareez of Persia are water management systems used to provide a reliable supply of water to human settlements or for irrigation in hot, arid and semi-arid climates. The deepest known qanat is in the Iranian city of Gonabad, which after 2700 years, still provides drinking and agricultural water to nearly 40... | Tunnel | Wikipedia | 505 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The world's oldest tunnel traversing under a water body is claimed to be the Terelek kaya tüneli under Kızıl River, a little south of the towns of Boyabat and Durağan in Turkey, just downstream from where Kizil River joins its tributary Gökırmak. The tunnel is presently under a narrow part of a lake formed by a dam som... | Tunnel | Wikipedia | 485 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The 1796 Stoddart Tunnel in Chapel-en-le-Frith in Derbyshire is reputed to be the oldest rail tunnel in the world. The rail wagons were originally horse-drawn.
Derby Tunnels in Salem, Massachusetts, were built in 1801 to smuggle imports affected by President Thomas Jefferson's new customs duties. Jefferson had ordered... | Tunnel | Wikipedia | 463 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The 1829 Wapping Tunnel in Liverpool, England, at long on a twin track railway, was the first rail tunnel bored under a metropolis. The tunnel's path is from Edge Hill in the east of the city to Wapping Dock in the south end Liverpool docks. The tunnel was used only for freight terminating at the Park Lane goods termi... | Tunnel | Wikipedia | 420 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The Victoria Tunnel Newcastle opened in 1842, is a subterranean wagonway with a maximum depth of that drops from entrance to exit. The tunnel runs under Newcastle upon Tyne, England, and originally exited at the River Tyne. It remains largely intact. Originally designed to carry coal from Spital Tongues to the river... | Tunnel | Wikipedia | 469 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The summit tunnel of the Semmering railway, the first Alpine tunnel, was opened in 1848 and was long. It connected rail traffic between Vienna, the capital of Austro-Hungarian Empire, and Trieste, its port.
The Giovi Rail Tunnel through the Appennini Mounts opened in 1854, linking the capital city of the Kingdom of S... | Tunnel | Wikipedia | 509 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
shield method of excavation;
permanent cast iron tunnel lining;
construction in a compressed air environment to inhibit water flowing through soft ground material into the tunnel heading.
Built in sections between 1890 and 1939, the section of London Underground's Northern line from Morden to East Finchley via Bank ... | Tunnel | Wikipedia | 256 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Longest
The Thirlmere Aqueduct in North West England, United Kingdom is sometimes considered the longest tunnel, of any type, in the world at , though the aqueduct's tunnel section is not continuous.
The Dahuofang Water Tunnel in China, opened in 2009, is the third longest water tunnel in the world at length.
Th... | Tunnel | Wikipedia | 324 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The Moffat Tunnel, opened in 1928, passes under the Continental Divide of the Americas in Colorado. The tunnel is long and at an elevation of is the highest active railroad tunnel in the U.S. (The inactive Tennessee Pass Line and the historic Alpine Tunnel are higher.)
Williamson's tunnels in Liverpool, from 1804 an... | Tunnel | Wikipedia | 499 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
The Eiksund Tunnel on national road Rv 653 in Norway is the world's deepest subsea road tunnel, measuring long, with deepest point at below the sea level, opened in February 2008.
Gerrards Cross railway tunnel, in England, opened in 2010, is notable in that it converted an existing railway cutting into a tunnel to c... | Tunnel | Wikipedia | 368 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Mining
The use of tunnels for mining is called drift mining. Drift mining can help find coal, goal, iron, and other minerals, just like normal mining.
Sub-surface mining consists of digging tunnels or shafts into the earth to reach buried ore deposits.
Military use
Some tunnels are not for transport at all but ra... | Tunnel | Wikipedia | 377 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Lava tubes are emptied lava conduits, formed during volcanic eruptions by flowing and cooling lava.
Natural Tunnel State Park (Virginia, US) features an natural tunnel, really a limestone cave, that has been used as a railroad tunnel since 1890.
Punarjani Guha in Kerala, India. Hindus believe that crawling through t... | Tunnel | Wikipedia | 457 | 160832 | https://en.wikipedia.org/wiki/Tunnel | Technology | Transport infrastructure | null | vital_articles |
Felt is a textile that is produced by matting, condensing, and pressing fibers together. Felt can be made of natural fibers such as wool or animal fur, or from synthetic fibers such as petroleum-based acrylic or acrylonitrile or wood pulp–based rayon. Blended fibers are also common. Natural fiber felt has special prope... | Felt | Wikipedia | 499 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
Dyes provided rich coloring, and colored slices of pre-felts (semi-felted sheets that could be cut in decorative ways) along with dyed yarns and threads were combined to create beautiful designs on the wool backgrounds. Felt was even used to create totems and amulets with protective functions. In traditional societies ... | Felt | Wikipedia | 444 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
In order to make multi-colored designs, felters conduct a two-step process in which they create pre-felts of specialized colors—these semi-completed sheets of colored felt can then be cut with a sharp implement (knife or scissors) and the distinctive colors placed next to each other as in making a mosaic. The felting p... | Felt | Wikipedia | 469 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
In Turkey, craft guilds called "ahi" came into being, and these groups were responsible for registering members and protecting the knowledge of felting. In Istanbul at one time, there were 1,000 felters working in 400 workshops registered in this ahi.
Needle felting
Needle felting is a method of creating felt that us... | Felt | Wikipedia | 407 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
Carroting
Invented in the mid 17th century and used until the mid-20th centuries, a process called "carroting" was used in the manufacture of good quality felt for making men's hats. Beaver, rabbit or hare skins were treated with a dilute solution of the mercury compound mercuric nitrate. The skins were dried in an ove... | Felt | Wikipedia | 459 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
Musical instruments
Many musical instruments use felt. It is often used as a damper. On drum cymbal stands, it protects the cymbal from cracking and ensures a clean sound. It is used to wrap bass drum strikers and timpani mallets. Felt is used extensively in pianos; for example, piano hammers are made of wool felt arou... | Felt | Wikipedia | 463 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
Modern day felters with access to a broad range of sheep and other animal fibers have exploited knowledge of these different breeds to produce special effects in their felt. Fleece locks are classified by the Bradford or Micron count, both which designate the fineness to coarseness of the material. Fine wools range fro... | Felt | Wikipedia | 200 | 160853 | https://en.wikipedia.org/wiki/Felt | Technology | Fabrics and fibers | null | vital_articles |
A cockpit or flight deck is the area, on the front part of an aircraft, spacecraft, or submersible, from which a pilot controls the vehicle.
The cockpit of an aircraft contains flight instruments on an instrument panel, and the controls that enable the pilot to fly the aircraft. In most airliners, a door separates the... | Cockpit | Wikipedia | 492 | 160878 | https://en.wikipedia.org/wiki/Cockpit | Technology | Aircraft components | null | vital_articles |
From about 1935, cockpit came to be used informally to refer to the driver's cabin, especially in high performance cars, and this is official terminology used to describe the compartment that the driver occupies in a Formula One car.
In an airliner, the cockpit is usually referred to as the flight deck, the term deriv... | Cockpit | Wikipedia | 446 | 160878 | https://en.wikipedia.org/wiki/Cockpit | Technology | Aircraft components | null | vital_articles |
In most cockpits the pilot's control column or joystick is located centrally (centre stick), although in some military fast jets the side-stick is located on the right hand side. In some commercial airliners (i.e.: Airbus—which features the glass cockpit concept) both pilots use a side-stick located on the outboard sid... | Cockpit | Wikipedia | 510 | 160878 | https://en.wikipedia.org/wiki/Cockpit | Technology | Aircraft components | null | vital_articles |
The layout of control panels in modern airliners has become largely unified across the industry. The majority of the systems-related controls (such as electrical, fuel, hydraulics and pressurization) for example, are usually located in the ceiling on an overhead panel. Radios are generally placed on a panel between the... | Cockpit | Wikipedia | 505 | 160878 | https://en.wikipedia.org/wiki/Cockpit | Technology | Aircraft components | null | vital_articles |
ND
A navigation display, which may be adjacent to the PFD, shows the route and information on the next waypoint, wind speed and wind direction. It may be pilot selectable to swap with the PFD.
EICAS/ECAM
The Engine Indication and Crew Alerting System (EICAS), used by Boeing and Embraer, or the Electronic Centralized A... | Cockpit | Wikipedia | 423 | 160878 | https://en.wikipedia.org/wiki/Cockpit | Technology | Aircraft components | null | vital_articles |
The fuselage (; from the French fuselé "spindle-shaped") is an aircraft's main body section. It holds crew, passengers, or cargo. In single-engine aircraft, it will usually contain an engine as well, although in some amphibious aircraft the single engine is mounted on a pylon attached to the fuselage, which in turn is ... | Fuselage | Wikipedia | 384 | 160891 | https://en.wikipedia.org/wiki/Fuselage | Technology | Aircraft components | null | vital_articles |
In this method, the exterior surface of the fuselage is also the primary structure. A typical early form of this (see the Lockheed Vega) was built using molded plywood, where the layers of plywood are formed over a "plug" or within a mold. A later form of this structure uses fiberglass cloth impregnated with polyester ... | Fuselage | Wikipedia | 484 | 160891 | https://en.wikipedia.org/wiki/Fuselage | Technology | Aircraft components | null | vital_articles |
Both monocoque and semi-monocoque are referred to as "stressed skin" structures as all or a portion of the external load (i.e. from wings and empennage, and from discrete masses such as the engine) is taken by the surface covering. In addition, all the load from internal pressurization is carried (as skin tension) by t... | Fuselage | Wikipedia | 476 | 160891 | https://en.wikipedia.org/wiki/Fuselage | Technology | Aircraft components | null | vital_articles |
Cabin windows, made from much lighter than glass stretched acrylic glass, consists of multiple panes: an outer one built to support four times the maximum cabin pressure, an inner one for redundancy and a scratch pane near the passenger. Acrylic is susceptible to crazing : a network of fine cracks appears but can be po... | Fuselage | Wikipedia | 254 | 160891 | https://en.wikipedia.org/wiki/Fuselage | Technology | Aircraft components | null | vital_articles |
In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating variability outside the up... | Box plot | Wikipedia | 391 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
Minimum (Q0 or 0th percentile): the lowest data point in the data set excluding any outliers
Maximum (Q4 or 100th percentile): the highest data point in the data set excluding any outliers
Median (Q2 or 50th percentile): the middle value in the data set
First quartile (Q1 or 25th percentile): also known as the lower... | Box plot | Wikipedia | 376 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
Another popular choice for the boundaries of the whiskers is based on the 1.5 IQR value. From above the upper quartile (Q3), a distance of 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed data point from the dataset that falls within this distance. Similarly, a distance of 1.5 times t... | Box plot | Wikipedia | 497 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
Notched box plots apply a "notch" or narrowing of the box around the median. Notches are useful in offering a rough guide of the significance of the difference of medians; if the notches of two boxes do not overlap, this will provide evidence of a statistically significant difference between the medians. The height of ... | Box plot | Wikipedia | 512 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
The median is the "middle" number of the ordered data set. This means that exactly 50% of the elements are below the median and 50% of the elements are greater than the median. The median of this ordered data set is 70°F.
The first quartile value (Q1 or 25th percentile) is the number that marks one quarter of the orde... | Box plot | Wikipedia | 501 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
Above is an example without outliers. Here is a followup example for generating box-plot with outliers:
The ordered set for the recorded temperatures is (°F): 52, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 89.
In this example, only the first and the last number are changed... | Box plot | Wikipedia | 401 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
Although box plots may seem more primitive than histograms or kernel density estimates, they do have a number of advantages. First, the box plot enables statisticians to do a quick graphical examination on one or more data sets. Box-plots also take up less space and are therefore particularly useful for comparing distr... | Box plot | Wikipedia | 178 | 160960 | https://en.wikipedia.org/wiki/Box%20plot | Mathematics | Statistics | null | vital_articles |
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-eth" item in a sequence.
Infinitesimals do not exist in the standard real ... | Infinitesimal | Wikipedia | 378 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
Infinitesimals are a basic ingredient in calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished fr... | Infinitesimal | Wikipedia | 350 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
The use of infinitesimals by Leibniz relied upon heuristic principles, such as the law of continuity: what succeeds for the finite numbers succeeds also for the infinite numbers and vice versa; and the transcendental law of homogeneity that specifies procedures for replacing expressions involving unassignable quantitie... | Infinitesimal | Wikipedia | 465 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
The English mathematician John Wallis introduced the expression 1/∞ in his 1655 book Treatise on the Conic Sections. The symbol, which denotes the reciprocal, or inverse, of ∞, is the symbolic representation of the mathematical concept of an infinitesimal. In his Treatise on the Conic Sections, Wallis also discusses th... | Infinitesimal | Wikipedia | 238 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
Prior to the invention of calculus mathematicians were able to calculate tangent lines using Pierre de Fermat's method of adequality and René Descartes' method of normals. There is debate among scholars as to whether the method was infinitesimal or algebraic in nature. When Newton and Leibniz invented the calculus, the... | Infinitesimal | Wikipedia | 341 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
First-order properties
In extending the real numbers to include infinite and infinitesimal quantities, one typically wishes to be as conservative as possible by not changing any of their elementary properties. This guarantees that as many familiar results as possible are still available. Typically, elementary means th... | Infinitesimal | Wikipedia | 351 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
An ordered field obeys all the usual axioms of the real number system that can be stated in first-order logic. For example, the commutativity axiom x + y = y + x holds.
A real closed field has all the first-order properties of the real number system, regardless of whether they are usually taken as axiomatic, for state... | Infinitesimal | Wikipedia | 345 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
Laurent series
An example from category 1 above is the field of Laurent series with a finite number of negative-power terms. For example, the Laurent series consisting only of the constant term 1 is identified with the real number 1, and the series with only the linear term x is thought of as the simplest infinitesima... | Infinitesimal | Wikipedia | 402 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
The most widespread technique for handling infinitesimals is the hyperreals, developed by Abraham Robinson in the 1960s. They fall into category 3 above, having been designed that way so all of classical analysis can be carried over from the reals. This property of being able to carry over all relations in a natural wa... | Infinitesimal | Wikipedia | 429 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
Infinitesimal delta functions
Cauchy used an infinitesimal to write down a unit impulse, infinitely tall and narrow Dirac-type delta function satisfying in a number of articles in 1827, see Laugwitz (1989). Cauchy defined an infinitesimal in 1821 (Cours d'Analyse) in terms of a sequence tending to zero. Namely, suc... | Infinitesimal | Wikipedia | 234 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
In 1936 Maltsev proved the compactness theorem. This theorem is fundamental for the existence of infinitesimals as it proves that it is possible to formalise them. A consequence of this theorem is that if there is a number system in which it is true that for any positive integer n there is a positive number x such that... | Infinitesimal | Wikipedia | 452 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
In 1977 Edward Nelson provided an answer following the second approach. The extended axioms are IST, which stands either for Internal set theory or for the initials of the three extra axioms: Idealization, Standardization, Transfer. In this system, we consider that the language is extended in such a way that we can exp... | Infinitesimal | Wikipedia | 475 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
An elementary calculus text based on smooth infinitesimal analysis is Bell, John L. (2008). A Primer of Infinitesimal Analysis, 2nd Edition. Cambridge University Press. ISBN 9780521887182.
A more recent calculus text utilizing infinitesimals is Dawson, C. Bryan (2022), Calculus Set Free: Infinitesimals to the Rescue,... | Infinitesimal | Wikipedia | 443 | 160990 | https://en.wikipedia.org/wiki/Infinitesimal | Mathematics | Basics_2 | null | vital_articles |
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
There are various types of generat... | Generating function | Wikipedia | 499 | 160993 | https://en.wikipedia.org/wiki/Generating%20function | Mathematics | Sequences and series | null | vital_articles |
Limitations
Not all expressions that are meaningful as functions of are meaningful as expressions designating formal series; for example, negative and fractional powers of are examples of functions that do not have a corresponding formal power series.
Types
Ordinary generating function (OGF)
When the term generati... | Generating function | Wikipedia | 490 | 160993 | https://en.wikipedia.org/wiki/Generating%20function | Mathematics | Sequences and series | null | vital_articles |
If is a Dirichlet character then its Dirichlet series generating function is called a Dirichlet -series. We also have a relation between the pair of coefficients in the Lambert series expansions above and their DGFs. Namely, we can prove that:
if and only if
where is the Riemann zeta function.
The sequence generate... | Generating function | Wikipedia | 487 | 160993 | https://en.wikipedia.org/wiki/Generating%20function | Mathematics | Sequences and series | null | vital_articles |
Examples of convolution polynomial sequences include the binomial power series, , so-termed tree polynomials, the Bell numbers, , the Laguerre polynomials, and the Stirling convolution polynomials.
Ordinary generating functions
Examples for simple sequences
Polynomials are a special case of ordinary generating func... | Generating function | Wikipedia | 511 | 160993 | https://en.wikipedia.org/wiki/Generating%20function | Mathematics | Sequences and series | null | vital_articles |
we can apply a well-known finite sum identity involving the Stirling numbers to obtain that
Rational functions
The ordinary generating function of a sequence can be expressed as a rational function (the ratio of two finite-degree polynomials) if and only if the sequence is a linear recursive sequence with constant c... | Generating function | Wikipedia | 404 | 160993 | https://en.wikipedia.org/wiki/Generating%20function | Mathematics | Sequences and series | null | vital_articles |
In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hy... | Statistical significance | Wikipedia | 491 | 160995 | https://en.wikipedia.org/wiki/Statistical%20significance | Mathematics | Statistics | null | vital_articles |
Related concepts
The significance level is the threshold for below which the null hypothesis is rejected even though by assumption it were true, and something else is going on. This means that is also the probability of mistakenly rejecting the null hypothesis, if the null hypothesis is true. This is also called fal... | Statistical significance | Wikipedia | 425 | 160995 | https://en.wikipedia.org/wiki/Statistical%20significance | Mathematics | Statistics | null | vital_articles |
The use of a one-tailed test is dependent on whether the research question or alternative hypothesis specifies a direction such as whether a group of objects is heavier or the performance of students on an assessment is better. A two-tailed test may still be used but it will be less powerful than a one-tailed test, bec... | Statistical significance | Wikipedia | 505 | 160995 | https://en.wikipedia.org/wiki/Statistical%20significance | Mathematics | Statistics | null | vital_articles |
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