History.

Antiquity.

Sockets in the walls around the paleolithic cave paintings at Lascaux, suggest that a scaffold system was used for painting the ceiling, over 17,000 years ago.  The Berlin Foundry Cup depicts scaffolding in ancient Greece (early 5th century BC). Egyptians, Nubians and Chinese are also recorded as having used scaffolding-like structures to build tall buildings. Early scaffolding was made of wood and secured with rope knots.

Modern era.

Scaffolding was erected by individual firms with wildly varying standards and sizes. The process was revolutionized by Daniel Palmer Jones and David Henry Jones. Modern day scaffolding standards, practices and processes can be attributed to these men and their companies: Rapid Scaffold Tie Company Ltd, Tubular Scaffolding Company and Scaffolding Great Britain Ltd (SGB).  David Palmer-Jones patented the "Scaffixer", a coupling device far more robust than rope which revolutionized scaffolding construction. In 1913, his company was commissioned for the reconstruction of Buckingham Palace, during which his Scaffixer gained much publicity. Palmer-Jones followed this up with the improved "Universal Coupler" in 1919 - this soon became the industry standard coupling and has remained so to this day.  Advancements in metallurgy throughout the early 20th century saw the introduction of tubular steel water pipes (instead of timber poles) with standardized dimensions, allowing for the industrial interchangeability of parts and improving the structural stability of the scaffold. The use of diagonal bracings also helped to improve stability, especially on tall buildings. The first frame system was brought to market by SGB in 1944 and was used extensively for the postwar reconstruction.

Scaffolding today.

The European Standard, BS EN 12811-1, specifies performance requirements and methods of structural and general design for access and working scaffolds. Requirements given are for scaffold structures that rely on the adjacent structures for stability. In general these requirements also apply to other types of working scaffolds.  The purpose of a working scaffold is to provide a safe working platform and access suitable for work crews to carry out their work. The European Standard sets out performance requirements for working scaffolds. These are substantially independent of the materials of which the scaffold is made. The standard is intended to be used as the basis for enquiry and design.

Materials.

The basic components of scaffolding are tubes, couplers and boards. The basic lightweight tube scaffolding that became the standard and revolutionised scaffolding, becoming the baseline for decades, was invented and marketed in the mid-1950s. With one basic 24 pound unit a scaffold of various sizes and heights could be assembled easily by a couple of labourers without the nuts or bolts previously needed.  Tubes are usually made either of steel or aluminium; although there is composite scaffolding which uses filament-wound tubes of glass fibre in a nylon or polyester matrix, because of the high cost of composite tube, it is usually only used when there is a risk from overhead electric cables that cannot be isolated. If steel, they are either 'black' or galvanised. The tubes come in a variety of lengths and a standard diameter of 48.3 mm. (1.5 NPS pipe). The chief difference between the two types of metal tubes is the lower weight of aluminium tubes (1.7 kg/m as opposed to 4.4 kg/m). However they are more flexible and have a lower resistance to stress. Tubes are generally bought in 6.3 m lengths and can then be cut down to certain typical sizes. Most large companies will brand their tubes with their name and address in order to deter theft.  Boards provide a working surface for scaffold users. They are seasoned wood and come in three thicknesses (38 mm (usual), 50 mm and 63 mm) are a standard width (225 mm) and are a maximum of 3.9 m long. The board ends are protected either by metal plates called hoop irons or sometimes nail plates, which often have the company name stamped into them. Timber scaffold boards in the UK should comply with the requirements of BS 2482. As well as timber, steel or aluminium decking is used, as well as laminate boards. In addition to the boards for the working platform, there are sole boards which are placed beneath the scaffolding if the surface is soft or otherwise suspect, although ordinary boards can also be used. Another solution, called a scaffpad, is made from a rubber base with a base plate moulded inside; these are desirable for use on uneven ground since they adapt, whereas sole boards may split and have to be replaced. Couplers are the fittings which hold the tubes together. The most common are called scaffold couplers, and there are three basic types: "right-angle couplers", "putlog couplers" and "swivel couplers". To join tubes end-to-end "joint pins" (also called spigots) or "sleeve couplers" are used. Only right angle couplers and swivel couplers can be used to fix tube in a 'load-bearing connection'. Single couplers are not load-bearing couplers and have no design capacity.  Other common scaffolding components include base plates, ladders, ropes, anchor ties, reveal ties, gin wheels, sheeting, etc. Most companies will adopt a specific colour to paint the scaffolding with, in order that quick visual identification can be made in case of theft. All components that are made from metal can be painted but items that are wooden should never be painted as this could hide defects. Despite the metric measurements given, many scaffolders measure tubes and boards in imperial units, with tubes from 21 feet down and boards from 13 ft down.  Bamboo scaffolding is widely used in Hong Kong and Macau, with nylon straps tied into knots as couplers. In India, bamboo or other wooden scaffolding is also mostly used, with poles being lashed together using ropes made from coconut hair (coir).

Basic scaffolding.

The key elements of the scaffolding are "the standard", "ledger" and "transoms". The standards, also called uprights, are the vertical tubes that transfer the entire weight of the structure to the ground where they rest on a square "base plate" to spread the load. The base plate has a shank in its centre to hold the tube and is sometimes pinned to a "sole board". Ledgers are horizontal tubes which connect between the standards. Transoms rest upon the ledgers at right angles. "Main transoms" are placed next to the standards, they hold the standards in place and provide support for boards; "intermediate transoms" are those placed between the main transoms to provide extra support for boards. In Canada this style is referred to as "English". "American" has the transoms attached to the standards and is used less but has certain advantages in some situations. As well as the tubes at right angles there are "cross braces" to increase rigidity, these are placed diagonally from ledger to ledger, next to the standards to which they are fitted. If the braces are fitted to the ledgers they are called ledger braces. To limit sway a "facade brace" is fitted to the face of the scaffold every 30 metres or so at an angle of 35°-55° running right from the base to the top of the scaffold and fixed at every level.  Of the couplers previously mentioned, right-angle couplers join ledgers or transoms to standards, putlog or single couplers join board bearing transoms to ledgers - Non-board bearing transoms should be fixed using a right-angle coupler. Swivel couplers are to connect tubes at any other angle. The actual joints are staggered to avoid occurring at the same level in neighbouring standards. The spacings of the basic elements in the scaffold are fairly standard. For a general purpose scaffold the maximum bay length is 2.1 m, for heavier work the bay size is reduced to 2 or even 1.8 m while for inspection a bay width of up to 2.7 m is allowed.  The scaffolding width is determined by the width of the boards, the minimum width allowed is 600 mm but a more typical four-board scaffold would be 870 mm wide from standard to standard. More heavy-duty scaffolding can require 5, 6 or even up to 8 boards width. Often an "inside board" is added to reduce the gap between the inner standard and the structure.  The lift height, the spacing between ledgers, is 2 m, although the base lift can be up to 2.7 m. The diagram above also shows a kicker lift, which is just 150 mm or so above the ground.  Transom spacing is determined by the thickness of the boards supported, 38 mm boards require a transom spacing of no more than 1.2 m while a 50 mm board can stand a transom spacing of 2.6 m and 63 mm boards can have a maximum span of 3.25 m. The minimum overhang for all boards is 50 mm and the maximum overhang is no more than 4x the thickness of the board.

Foundations.

Good foundations are essential. Often scaffold frameworks will require more than simple base plates to safely carry and spread the load. Scaffolding can be used without base plates on concrete or similar hard surfaces, although base plates are always recommended. For surfaces like pavements or tarmac base plates are necessary. For softer or more doubtful surfaces sole boards must be used, beneath a single standard a sole board should be at least with no dimension less than, the thickness must be at least. For heavier duty scaffold much more substantial baulks set in concrete can be required. On uneven ground steps must be cut for the base plates, a minimum step size of around is recommended. A working platform requires certain other elements to be safe. They must be close-boarded, have double guard rails and toe and stop boards. Safe and secure access must also be provided.

Ties.

Scaffolds are only rarely independent structures. To provide stability for a scaffolding (at left) framework ties are generally fixed to the adjacent building/fabric/steelwork.  General practice is to attach a tie every 4 m on alternate lifts (traditional scaffolding). Prefabricated System scaffolds require structural connections at all frames - i.e. 2–3 m centres (tie patterns must be provided by the System manufacturer/supplier). The ties are coupled to the scaffold as close to the junction of standard and ledger (node point) as possible. Due to recent regulation changes, scaffolding ties must support +/- loads (tie/butt loads) and lateral (shear) loads.  Due to the different nature of structures there is a variety of different ties to take advantage of the opportunities.  "Through ties" are put through structure openings such as windows. A vertical inside tube crossing the opening is attached to the scaffold by a transom and a crossing horizontal tube on the outside called a bridle tube. The gaps between the tubes and the structure surfaces are packed or wedged with timber sections to ensure a solid fit.  "Box ties" are used to attach the scaffold to suitable pillars or comparable features. Two additional transoms are put across from the lift on each side of the feature and are joined on both sides with shorter tubes called tie tubes. When a complete box tie is impossible a l-shaped "lip tie" can be used to hook the scaffold to the structure, to limit inward movement an additional transom, a "butt transom", is placed hard against the outside face of the structure.  Sometimes it is possible to use "anchor ties" (also called "bolt ties"), these are ties fitted into holes drilled in the structure. A common type is a ring bolt with an expanding wedge which is then tied to a node point. The least 'invasive' tie is a "reveal tie". These use an opening in the structure but use a tube wedged horizontally in the opening. The reveal tube is usually held in place by a reveal screw pin (an adjustable threaded bar) and protective packing at either end. A transom tie tube links the reveal tube to the scaffold. Reveal ties are not well regarded, they rely solely on friction and need regular checking so it is not recommended that more than half of all ties be reveal ties.  If it is not possible to use a safe number of ties "rakers" can be used. These are single tubes attached to a ledger extending out from the scaffold at an angle of less than 75° and securely founded. A transom at the base then completes a triangle back to the base of the main scaffold.

Bamboo scaffolding.

Bamboo scaffolding is a type of scaffolding made from bamboo and widely used in construction work for centuries. Many famous landmarks, notably The Great Wall of China, were built using bamboo scaffolding, and its use continues today in some parts of the world.

History.

Bamboo Scaffolding was first introduced into the building industry in Hong Kong immediately after colonization in the 1800s. It was widely used in the building of houses and multi-story buildings (up to four stories high) prior to the development of metal scaffolding. It was also useful for short-term construction projects, such as framework for temporary sheds for Cantonese Opera performances. There are three types of scaffolding in Hong Kong:

Gradual decline.

In 2013, there were 1,751 registered bamboo scaffolders and roughly 200 scaffolding companies in Hong Kong. The use of bamboo scaffolding is diminishing due to shortages in labor and material. Despite the lack of labor force and material, recently safety issues have become another serious concern.  The labor shortage may be due to the reluctance of younger generations to become scaffolders. “They even think that it’s a dirty and dangerous job. They are not going to do that kind of work,” said Yu Hang Flord, who has been a scaffolder for 30 years and later became the director of Wui Fai Holdings, a member of the Hong Kong and Kowloon Scaffolders General Merchants Association. “They refuse to step in, although we give them high pay. They are scared of it. Young generations do not like jobs that involve hard work.” Another reason fewer people are becoming scaffolders is that new recruits need to undergo training with the Hong Kong Construction Industry Council in order to acquire a license. Older scaffolders generally learned in apprenticeships, and may have been able to gather more hands-on experience.  Material shortages are also a contributing factor to the decline. The bamboo scaffolding material was imported from mainland China. Bamboo—which matures after three years to the wide diameter and thick skin perfect for scaffolding—came from the Shaoxing area in Guangdong. Over the past two decades, firms have had to look to Guangxi instead. The industry's fear is that one day supplies will be blocked due to export embargoes and environmental concerns. Attempts to import bamboo from Thailand, or switch to synthetic or plastic bamboo, have so far proved unsuccessful.  In many African countries, notably Nigeria, bamboo scaffolding is still used for small scale construction in urban areas. In rural areas, the use of bamboo scaffolding for construction is common. In fact, bamboo is an essential building and construction commodity in Nigeria; the bamboo materials are transported on heavy trucks and trailers from rural areas (especially the tropical rain forest) to cities and the northern part of Nigeria.  Some of the structures in relaxation and recreation centres, both in urban and rural areas of Nigeria, are put in place using bamboo materials. This is not for reasons of poverty (especially in the cities) but to add more aesthetics to these centres. Bamboo materials are still used in the construction of some bukas (local restaurants) in rural areas.

Specifications.

Forms of bamboo scaffolding include: Only double-row bamboo scaffold is allowed to be used for working at height. The perimeter of bamboo scaffold should be covered by nylon mesh against falling objects. The lapping of nylon mesh should be at least 100 mm wide. Suitable means of access should be provided from the building or ground level to the scaffold such as gangway, stairs and ladder etc. Sloping catch fans shall be erected at a level close to the first floor and at no more than 15 metres, vertical intervals should give a minimum horizontal protection coverage of 1500 mm. Large catch fans should be erected at specific locations to protect the public and/or workers underneath. A suitable receptacle, covered with galvanized zinc sheet, should be provided within each catch-fan to trap falling objects. Steel brackets shall be provided for supporting the standard of scaffold at about six floor intervals. The horizontal distance between steel brackets is about 3 metres. Mild steel bars or similar materials are required to tie any structure to maintain the bamboo scaffold in its position on every floor. The distance of adjacent putlogs is about 3 to 4 metres. Every working platform must be at least 400 mm wide and closely boarded by planks. The edges of working platforms should be protected by no less than 2 horizontal bamboo members of the scaffold, at intervals between 750 mm to 900 mm and suitable toe-boards no less than 200 mm high. All scaffolds with a height excess of 15 metres shall be designed by an Engineer. They should complete a formal training in bamboo scaffolding work or hold a trade test certificate on bamboo scaffolding and have at least 10 years of relevant experience. They should complete formal training in bamboo scaffolding work or hold a trade test certificate on bamboo scaffolding and have at least 3 years of relevant experience.

Uses in construction.

Bamboo scaffolding is a temporary structure to support people and materials when constructing or repairing building exteriors and interiors. In bamboo scaffolding, plastic fibre straps and bamboo shoots are bound together to form a solid and secure scaffold structure without screws. Bamboo scaffolding does not need to have a foundation on the ground, as long as the scaffolding has a fulcrum for structural support.  Bamboo scaffolding is mostly seen in developing Asian countries such as India, Bangladesh, Sri Lanka, and Indonesia.

Chinese opera theatres.

Chinese Opera is one of the world's "Intangible Cultural Heritages". One of bamboo scaffolding's main alternative uses is in drama theatres. The flexibility and convenience of this type of scaffolding suits stages set up for temporary use and also separates the audience from the performers.  Respecting and promoting the traditional cultures of Chinese Opera, a huge event called the West Kowloon Bamboo Theatre has been held at the West Kowloon Waterfront Promenade annually since 2012.

Yu Lan Ghost Festival.

Stages are built from bamboo scaffolding for the live Chinese operas and Chiu Chow–style dramas performed during every Yu Lan Ghost Festival to worship ghostly ancestors.

Cheung Chau Bun Festival.

The bamboo tower used in the famous Bun Scrambling Competition during the Cheung Chau Bun Festival on the island of Cheung Chau is constructed out of bamboo scaffolding. Nine thousand buns, representing fortune and blessing, are supported on the fourteen-meter tall bamboo tower in front of the Pak Tai Temple. For the Piu Sik Parade, bamboo stands and racks are used to hold the young costumed performers above the crowds.

Specialty scaffolding.

Types of scaffolding covered by the Occupational Health and Safety Administration in the United States include the following categories: Pole; tube and coupler; fabricated frame (tubular welded frame scaffolds); plasterers’, decorators’, and large area scaffolds; bricklayers' (pipe); horse; form scaffolds and carpenters’ bracket scaffolds; roof brackets; outrigger; pump jacks; ladder jacks; window jacks; crawlingboards (chicken ladders); step, platform, and trestle ladder scaffolds; single-point adjustable suspension; two-point adjustable suspension (swing stages); multipoint adjustable suspension; stonesetters’ multipoint adjustable suspension scaffolds, and masons’ multipoint adjustable suspension scaffolds; catenary; float (ship); interior hung; needle beam; multilevel suspended; mobile; repair bracket scaffolds; and stilts.

Putlog scaffold.

In addition to the putlog couplers (discussed above), there are also putlog tubes. These have a flattened end or have been fitted with a blade. This feature allows the end of the tube to be inserted into or rest upon the brickwork of the structure.  A putlog scaffold may also be called a bricklayer's scaffold. As such, the scaffold consists only of a single row of standards with a single ledger. The putlogs are transoms - attached to the ledger at one end but integrated into the bricks at the other.  Spacing is the same on a putlog scaffold as on a general purpose scaffold, and ties are still required. In recent years a number of new innovations have meant an increased scope of use for scaffolding, such as ladderbeams for spanning spaces that cannot accommodate standards and the increased use of sheeting and structure to create temporary roofs.

Pump-jack.

A pump-jack is a type of portable scaffolding system. The scaffold rests on supports attached to two or more vertical posts. The user raises the scaffolding by pumping the foot pedals on the supports, like an automobile jack.

Baker staging.

Baker staging is a metal scaffold which is easy to assemble. Rolling platforms typically wide by long and tall sections which can be stacked up to three high with the use of added outriggers. The work platform height is adjustable.

X-Deck ladder scaffolding.

Low level scaffolding that is height adjustable. It is a hybrid ladder scaffold work platform.

Standards.

The widespread use of scaffolding systems, along with the profound importance that they earned in modern applications such as civil engineering projects and temporary structures, led to the definition of a series of standards covering a vast number of specific issues involving scaffolding. Among the standards there are:

Scaffolding, also called scaffold or staging, is a temporary structure used to support a work crew and materials to aid in the construction, maintenance and repair of buildings, bridges and all other man-made structures. Scaffolds are widely used on site to get access to heights and areas that would be otherwise hard to get to. Unsafe scaffolding has the potential to result in death or serious injury. Scaffolding is also used in adapted forms for formwork and shoring, grandstand seating, concert stages, access/viewing towers, exhibition stands, ski ramps, half pipes and art projects.

Lešení je dočasná stavební konstrukce, která se zřizuje na staveništích pro pomoc při práci ve výškách vně i uvnitř budovy. Všeobecná pravidla určují, že lešení by mělo být co nejjednodušší, bezpečné a mělo by mít dostatečnou nosnost. Lešení se rozlišuje podle konstrukce a tvaru na systémová, trubková a pojízdná. Další rozlišení spočívá v materiálu, z něhož je lešení vyrobeno. Liší se především podle druhu využití.


Types.

Sedimentary.

Sedimentary breccia is a type of clastic sedimentary rock which is made of angular to subangular, randomly oriented clasts of other sedimentary rocks. A conglomerate, by contrast, is a sedimentary rock composed of rounded fragments or clasts of pre-existing rocks. Both breccia and conglomerate are composed of fragments averaging greater than in size. The angular shape of the fragments indicates that the material has not been transported far from its source.  Sedimentary breccia consists of angular, poorly sorted, immature fragments of rocks in a finer grained groundmass which are produced by mass wasting. It is lithified colluvium or scree. Thick sequences of sedimentary (colluvial) breccia are generally formed next to fault scarps in grabens. Breccia may occur along a buried stream channel where it indicates accumulation along a juvenile or rapidly flowing stream. Sedimentary breccia may be formed by submarine debris flows. Turbidites occur as fine-grained peripheral deposits to sedimentary breccia flows. In a karst terrain, a collapse breccia may form due to collapse of rock into a sinkhole or in cave development.

Fault.

Fault breccia results from the grinding action of two fault blocks as they slide past each other. Subsequent cementation of these broken fragments may occur by means of the introduction of mineral matter in groundwater.

Igneous.

Igneous clastic rocks can be divided into two classes:

Volcanic.

Volcanic pyroclastic rocks are formed by explosive eruption of lava and any rocks which are entrained within the eruptive column. This may include rocks plucked off the wall of the magma conduit, or physically picked up by the ensuing pyroclastic surge. Lavas, especially rhyolite and dacite flows, tend to form clastic volcanic rocks by a process known as "autobrecciation". This occurs when the thick, nearly solid lava breaks up into blocks and these blocks are then reincorporated into the lava flow again and mixed in with the remaining liquid magma. The resulting breccia is uniform in rock type and chemical composition.  Lavas may also pick up rock fragments, especially if flowing over unconsolidated rubble on the flanks of a volcano, and these form volcanic breccias, also called pillow breccias. Within the volcanic conduits of explosive volcanoes the volcanic breccia environment merges into the intrusive breccia environment. There the upwelling lava tends to solidify during quiescent intervals only to be shattered by ensuing eruptions.

Intrusive.

Clastic rocks are also commonly found in shallow subvolcanic intrusions such as porphyry stocks, granites and kimberlite pipes, where they are transitional with volcanic breccias. Intrusive rocks can become brecciated in appearance by multiple stages of intrusion, especially if fresh magma is intruded into partly consolidated or solidified magma. This may be seen in many granite intrusions where later aplite veins form a late-stage stockwork through earlier phases of the granite mass. When particularly intense, the rock may appear as a chaotic breccia.  Clastic rocks in mafic and ultramafic intrusions have been found and form via several processes:

Impact.

Impact breccias are thought to be diagnostic of an impact event such as an asteroid or comet striking the Earth and are normally found at impact craters. Impact breccia, a type of impactite, forms during the process of impact cratering when large meteorites or comets impact with the Earth or other rocky planets or asteroids. Breccia of this type may be present on or beneath the floor of the crater, in the rim, or in the ejecta expelled beyond the crater.  Impact breccia may be identified by its occurrence in or around a known impact crater, and/or an association with other products of impact cratering such as shatter cones, impact glass, shocked minerals, and chemical and isotopic evidence of contamination with extraterrestrial material (e.g., iridium and osmium anomalies). An example of an impact breccia is the Neugrund breccia, which was formed in the Neugrund impact.

Hydrothermal.

Hydrothermal breccias usually form at shallow crustal levels (<1 km) between 150 and 350 °C, when seismic or volcanic activity causes a void to open along a fault deep underground. The void draws in hot water, and as pressure in the cavity drops, the water violently boils. In addition, the sudden opening of a cavity causes rock at the sides of the fault to destabilise and implode inwards, and the broken rock gets caught up in a churning mixture of rock, steam and boiling water. Rock fragments collide with each other and the sides of the void, and the angular fragments become more rounded. Volatile gases are lost to the steam phase as boiling continues, in particular carbon dioxide. As a result, the chemistry of the fluids changes and ore minerals rapidly precipitate. Breccia-hosted ore deposits are quite common.  The morphology of breccias associated with ore deposits varies from tabular sheeted veins and clastic dikes associated with overpressured sedimentary strata, to large-scale intrusive diatreme breccias (breccia pipes), or even some synsedimentary diatremes formed solely by the overpressure of pore fluid within sedimentary basins. Hydrothermal breccias are usually formed by hydrofracturing of rocks by highly pressured hydrothermal fluids. They are typical of the epithermal ore environment and are intimately associated with intrusive-related ore deposits such as skarns, greisens and porphyry-related mineralisation. Epithermal deposits are mined for copper, silver and gold.  In the mesothermal regime, at much greater depths, fluids under lithostatic pressure can be released during seismic activity associated with mountain building. The pressurised fluids ascend towards shallower crustal levels that are under lower hydrostatic pressure. On their journey, high-pressure fluids crack rock by hydrofracturing, forming an angular "in situ" breccia. Rounding of rock fragments is less common in the mesothermal regime, as the formational event is brief. If boiling occurs, methane and hydrogen sulfide may be lost to the steam phase, and ore may precipitate. Mesothermal deposits are often mined for gold.

Ornamental uses.

For thousands of years, the striking visual appearance of breccias has made them a popular sculptural and architectural material. Breccia was used for column bases in the Minoan palace of Knossos on Crete in about 1800 BC. Breccia was used on a limited scale by the ancient Egyptians; one of the best-known examples is the statue of the goddess Tawaret in the British Museum. It was regarded by the Romans as an especially precious stone and was often used in high-profile public buildings. Many types of marble are brecciated, such as Breccia Oniciata or Breche Nouvelle.  Breccia is most often used as an ornamental or facing material in walls and columns. A particularly striking example can be seen in the Pantheon in Rome, which features two gigantic columns of pavonazzetto, a breccia from Phrygia (in modern Turkey). Pavonazzetto obtains its name from its extremely colourful appearance, which is reminiscent of a peacock's feathers ("pavone" is "peacock" in Italian).

Breccia ( or ) is a rock composed of broken fragments of minerals or rock cemented together by a fine-grained matrix that can be similar to or different from the composition of the fragments.

Brekcie je sedimentární hornina, která vzniká buď ledovcovým, nebo suchozemským způsobem. Její zrnitost je hrubá. Brekcie má proměnlivou barvu, která závisí na minerálním složení. Brekcie je tvořena ostrohrannými úlomky minerálů a hornin. Vzácně se uvnitř brekcií vyskytují zkameněliny.


Background.

Given the period when he was alive, Adelard's biography is incomplete in places and leaves some aspects open to interpretation. As a result, much of what is ascribed to Adelard is a product of his own testimony. As his name suggests, he was born in the Roman English city of Bath but how he lived is not entirely known. Despite his extensive travels, by the end of his life he had returned to Bath, where he died. Scholars are hesitant to ascribe definitive parents to the philosopher but Fastred, a tenant of the Bishop of Wells, is mostly plausibly identified as this figure. His name (Adelard) is of Anglo-Saxon origin, which would have placed him in the subordinate class, status wise, in 11th-century England. It is believed that he left England toward the end of the 11th century for Tours, likely on the advice of Bishop John de Villula, who had moved the seat of his bishopric from Wells to Bath in 1090. During his studies in Tours, an anonymous "wise man of Tours" inspired Adelard with his interest in astronomy to study the science. Adelard later taught for a time at Laon, leaving Laon for travel no later than 1109. After leaving Laon, he travelled to Southern Italy and Sicily no later than 1116.  Adelard also travelled extensively throughout the "lands of the Crusades": Greece, West Asia, Sicily, Spain, Tarsus, Antioch and potentially Palestine. The time spent in these areas would help explain his fascination with mathematics and his access to Arabic scholars. By 1126, Adelard returned to the West with the intention of spreading the knowledge he had gained about Arab astronomy and geometry to the Latin world. One aspect of particular interest with respect to Adelard, his teachings, and the time period he grew up, was the relation to the Crusades. This time of remarkable transition marked an opportunity for someone to gain valuable influence over the evolution of human history. While the Crusades offered little in the way of a victor, Adelard's non-discriminatory scholarly work inspired him to bring back to England many ancient texts and new questions that would later give rise to an English Renaissance. Again, given the 11th-century time period that Adelard was alive, it was understandably difficult for Adelard to have achieved his educational pursuits. In the absence of a printing press and given the weak public literacy rate, books were rare items in medieval Europe—generally held only by royal courts or Catholic monastic communities (Kraye, "et al." 1987). Fittingly, Adelard studied with monks at the Benedictine Monastery at Bath Cathedral.

Main works.

Among Adelard of Bath's original works is a trio of dialogues, written to mimic the Platonic style, or correspondences with his nephew. The earliest of these is "De Eodem et Diverso (On the Same and the Different)". It is written in the style of a protreptic, or an exhortation to the study of philosophy. The work is modelled on Boethius' "Consolation of Philosophy", evident in Adelard's vocabulary and phraseology. It is believed to have been written near Tours after he had already travelled, though there is no indication that he had travelled past Southern Italy and Sicily at the time of writing. The work takes the form of a dramatic dialogue between Philocosmia, who advocates worldly pleasures, and Philosophia, whose defence of scholarship leads into a summary of the seven liberal arts. Underlining the entire work is the contrast between Philocosmia's "res" (perceptible reality), and Philosophia's "verba" (mental concepts). Each section of the liberal arts is divided into two parts. Presented first is a description of the allegorical figure representing the art, in which the importance of that art is indicated, followed by a summary of the doctrines of that art, as told by the allegorical figure who is presented as the founder or main proponent of the particular art.  The second of this trio, and arguably Adelard's most significant contribution, was his "Questiones Naturales" or "Questions on Natural Science". It can be dated between 1107 and 1133 as, in the text, Adelard himself mentions that seven years have passed since his lecturing in schools at Laon. He chooses to present this work as a forum for Arabic learning, referring often to his experiences in Antioch. He sets out seventy-six questions, in the form of a Platonic dialogue about meteorology and natural science. It was used heavily in schools into and beyond the 13th century but the teaching on natural things would ultimately be superseded by Aristotle's writing. The text is broken up into three parts: "On Plants and Brute Animals", "On Man" and "On Earth, Water, Air, and Fire". Two of the more specific features associated with this text are (1) a preference for reason over authority in matters of science and nature (in other words, seeking solutions via reason and logic rather than through faith) and (2) the use of the literary device of invoking Arab teachings when presenting very controversial topics (e.g. that brute animals may possess knowledge and souls) Adelard didn't think that the use of reason to seek knowledge was in any way contradictory with Christian faith in God. The soul is a large part of the dialogue in this text as "On Man" discusses a corporeal soul in man, while the final section elaborates on the incorporeal soul of elements and animals. "Questiones Naturales" appears to have been an immediate success as it was copied on both sides of the English Channel and was even presented in a "pocket-book" format, suggesting that it was meant to be carried around.  The final section in his trilogy is a treatise on hawking called "De Avibus Tractatus (Treatise on Birds)". It is a medical text that addresses disease from head-to-toe. While it has been argued that this treatise was not widely distributed, an investigation of later Latin and French treatises reveals a number of excerpts from Adelard's work.  The remainder of Adelard's original works did not involve the persona of his nephew. He wrote a treatise on the use of the abacus called "Regulae Abaci", which was likely written very early in his career because it shows no trace of Arab influence. This treatise is believed to be proof that Adelard was connected to the Exchequer table that was used for monetary calculations in the medieval period. If you read the source quoted, its obvious Adelard of Bath probably knew who worked at the Exchequer and might have met them at Laon, but what is common among them is that their educations are in Laon! Further evidence for this can be found in the Pipe Roll of Henry I, which shows that he had received a discharge from the murder fine (a fine levied on inhabitants of a certain area based on the murder of a Norman that occurred in a generally accessible field in that same area) levied on the community of Wiltshire in 1130, though there is no other proof for this fact. There is a debate about if the Adelard who lived in Bath and was levied with a murder-charge really is the same Adelard as Adelard of Bath, who is not famous for his violence. The work that Adelard of Bath is known for in the Latin world is his translation of the astronomical tables of al-Khwarizmi, the first widely accessible Latin translation of the Islamic ideas about algebra. In the Middle Ages he was known for his rediscovery and teaching of geometry, earning his reputation when he made the first full translation of Euclid's ""Elements"" and began the process of interpreting the text for a Western audience.

Influence.

When Adelard's influence on the study of philosophy is considered, it is clear that his ideas most notably manifested in the later works of Robert Grosseteste and Roger Bacon. While his work in natural philosophy is probably overshadowed by Aristotle, it still helped lay the foundations for much of the progress that was made in the later centuries. His work surrounding Euclid's "Elements", for example, was of great help in providing training that would help future scholars understand the relationships between demonstrative and geometrical proofs. While his original writings demonstrate that he had a sincere passion for the seven liberal arts (grammar, rhetoric, logic, mathematics, geometry, music, and astronomy), his work in "Quaestiones naturales" illustrated a more encompassing dedication to subjects such as physics, the natural sciences, and possibly even metaphysics. His influence is also evident in "De philosophia mundi" by William of Conches, Hugh of Saint Victor, and Isaac of Stella's "Letters to Alcher on the Soul". He introduced algebra to the Latin world and his commentaries in Version III of Euclid's "Elements" were extremely influential in the 13th century. Adelard also displays original thought of a scientific bent, raising the question of the shape of the Earth (he believed it round) and the question of how it remains stationary in space, and also the interesting question of how far a rock would fall if a hole were drilled through the Earth and a rock dropped through it, see center of gravity. Campanus of Novara probably had access to Adelard's translation of "Elements", and it is Campanus' edition that was first published in Venice in 1482 after the invention of the printing press. It became the chief textbook of the mathematical schools of Western Europe until the 16th century.

Adelard of Bath (; 1080 1152 AD) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Arabic and Greek scientific works of astrology, astronomy, philosophy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. He is known as one of the first to introduce the Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East.

Adelard z Bathu (asi 1080 - asi 1160) byl cestovatel, filosof, překladatel, matematik, geometr, astronom a astrolog. Procestoval minimálně Sicílií a Sýrii. Díky znalosti arabštiny později přeložil do latiny stěžejní díla z geometrie a astronomie (např. "Základy" od Eukleida či "Astronomické tabulky" od al-Chwárizmího). Pracoval na pojednání o sokolnictví, o použití astrolábu a abacusu. Sestavil několik horoskopů pro anglickou královskou rodinu, které se zachovaly dodnes v Britské knihovně.


Summary.

Basic concepts.

Although not a detailed study of Protestantism but rather an introduction to Weber's later studies of interaction between various religious ideas and economics ("," "," and "Ancient Judaism)," "The Protestant Ethic and the Spirit of Capitalism" argues that Puritan ethics and ideas influenced the development of capitalism. The'spirit of capitalism' does not refer to the spirit in the metaphysical sense but rather a set of values, the spirit of hard work and progress.  Religious devotion, Weber argues, is usually accompanied by a rejection of worldly affairs, including the pursuit of wealth and possessions. To illustrate his theory, Weber quotes the ethical writings of Benjamin Franklin:  Weber notes that this is not a philosophy of mere greed, but a statement laden with moral language. Indeed, Franklin claims that God revealed the usefulness of virtue to him.  The Reformation profoundly affected the view of work, dignifying even the most mundane professions as adding to the common good and thus blessed by God, as much as any "sacred" calling (German: "Ruf"). A common illustration is that of a cobbler, hunched over his work, who devotes his entire effort to the praise of God.  To emphasize the work ethic in Protestantism relative to Catholics, he notes a common problem that industrialists face when employing precapitalist laborers: Agricultural entrepreneurs will try to encourage time spent harvesting by offering a higher wage, with the expectation that laborers will see time spent working as more valuable and so engage it longer. However, in precapitalist societies this often results in laborers spending "less" time harvesting. Laborers judge that they can earn the same, while spending less time working and having more leisure. He also notes that societies having more Protestants are those that have a more developed capitalist economy.  It is particularly advantageous in technical occupations for workers to be extremely devoted to their craft. To view the craft as an end in itself, or as a "calling" would serve this need well. This attitude is well-noted in certain classes which have endured religious education, especially of a Pietist background.  He defines the spirit of capitalism as the ideas and "esprit" that favour the rational pursuit of economic gain: "We shall nevertheless provisionally use the expression'spirit of capitalism' for that attitude which, "in the pursuit of a calling [berufsmäßig]", strives systematically for profit for its own sake in the manner exemplified by Benjamin Franklin."  Weber points out that such a spirit is not limited to Western culture if one considers it as the attitude of individuals, but that such individuals – heroic entrepreneurs, as he calls them – could not by themselves establish a new economic order (capitalism). He further noted that the spirit of capitalism could be divorced from religion, and that those passionate capitalists of his era were either passionate against the Church or at least indifferent to it. Desire for profit with minimum effort and seeing work as a burden to be avoided, and doing no more than what was enough for modest life, were common attitudes. As he wrote in his essays:  After defining the "spirit of capitalism," Weber argues that there are many reasons to find its origins in the religious ideas of the Reformation. Many others like William Petty, Montesquieu, Henry Thomas Buckle, John Keats have noted the affinity between Protestantism and the development of commercialism.  Weber shows that certain branches of Protestantism had supported worldly activities dedicated to economic gain, seeing them as endowed with moral and spiritual significance. This recognition was not a goal in itself; rather they were a byproduct of other doctrines of faith that encouraged planning, hard work and self-denial in the pursuit of worldly riches.

Origins of the Protestant work ethic.

Weber traced the origins of the Protestant ethic to the Reformation, though he acknowledged some respect for secular everyday labor as early as the Middle Ages. The Roman Catholic Church assured salvation to individuals who accepted the church's sacraments and submitted to the clerical authority. However, the Reformation had effectively removed such assurances. From a psychological viewpoint, the average person had difficulty adjusting to this new worldview, and only the most devout believers or "religious geniuses" within Protestantism, such as Martin Luther, were able to make this adjustment, according to Weber.  In the absence of such assurances from religious authority, Weber argued that Protestants began to look for other "signs" that they were saved. Calvin and his followers taught a doctrine of double predestination, in which from the beginning God chose some people for salvation and others for damnation. The inability to influence one's own salvation presented a very difficult problem for Calvin's followers. It became an absolute duty to believe that one was chosen for salvation, and to dispel any doubt about that: lack of self-confidence was evidence of insufficient faith and a sign of damnation. So, self-confidence took the place of priestly assurance of God's grace.  Worldly success became one measure of that self-confidence. Luther made an early endorsement of Europe's emerging divisions. Weber identifies the applicability of Luther's conclusions, noting that a "vocation" from God was no longer limited to the clergy or church, but applied to any occupation or trade. Weber had always detested Lutheranism for the servility it inspired toward the bureaucratic state. When he discussed it in the "Protestant Ethic", he used Lutheranism as the chief example of the "unio mystica" that contrasted sharply with the ascetic posture. Later he would associate "Luther, the symbolic exponent of bureaucratic despotism, with the ascetic hostility to Eros — an example of Weber's sporadic tendency to link together bureaucratic and ascetic modes of life and to oppose both from mystical and aristocratic perspectives."  However, Weber saw the fulfillment of the Protestant ethic not in Lutheranism, which was too concerned with the reception of divine spirit in the soul, but in Calvinistic forms of Christianity. The trend was carried further still in Pietism. The Baptists diluted the concept of the calling relative to Calvinists, but other aspects made its congregants fertile soil for the development of capitalism—namely, a lack of paralyzing ascetism, the refusal to accept state office and thereby develop "un"politically, and the doctrine of control by conscience which caused rigorous honesty.  What Weber argued, in simple terms:  The manner in which this dilemma was resolved, Weber argued, was the investment of this money, which gave an extreme boost to nascent capitalism.

Protestant work ethic in Weber's time.

By the time Weber wrote his essay, he believed that the religious underpinnings of the Protestant ethic had largely gone from society. He cited the writings of Benjamin Franklin, which emphasized frugality, hard work and thrift, but were mostly free of spiritual content. Weber also attributed the success of mass production partly to the Protestant ethic. Only after expensive luxuries were disdained could individuals accept the uniform products, such as clothes and furniture, that industrialization offered.  In his conclusion to the book, Weber lamented that the loss of religious underpinning to capitalism's spirit has led to a kind of involuntary servitude to mechanized industry.  Weber maintained that while Puritan religious ideas had significantly impacted the development of economic system in Europe and United States, there were other factors in play, as well. They included a closer relationship between mathematics and observation, the enhanced value of scholarship, rational systematization of government administration, and an increase in entrepreneurship ventures. In the end, the study of Protestant ethic, according to Weber, investigated a part of the detachment from magic, that "disenchantment of the world" that could be seen as a unique characteristic of Western culture.

Conclusions.

In the final endnotes Weber states that he abandoned research into Protestantism because his colleague Ernst Troeltsch, a professional theologian, had begun work on "The Social Teachings of the Christian Churches and Sects". Another reason for Weber's decision was that Troeltsch's work already achieved what he desired in that area, which is laying groundwork for comparative analysis of religion and society. Weber moved beyond Protestantism with his research but would continue research into sociology of religion within his later works (the study of Judaism and the religions of and ).  This book is also Weber's first brush with the concept of rationalization. His idea of modern capitalism as growing out of the religious pursuit of wealth meant a change to a rational means of existence, wealth. That is to say, at some point the Calvinist rationale informing the "spirit" of capitalism became unreliant on the underlying religious movement behind it, leaving only rational capitalism. In essence then, Weber's "Spirit of Capitalism" is effectively and more broadly a Spirit of Rationalization.

Reception.

The essay can also be interpreted as one of Weber's criticism of Karl Marx and his theories. While Marx's historical materialism held that all human institutions – including religion – were based on economic foundations, many have seen "The Protestant Ethic" as turning this theory on its head by implying that a religious movement fostered capitalism, not the other way around.  Other scholars have taken a more nuanced view of Weber's argument. Weber states in the closing of this essay, "it is, of course, not my aim to substitute for a one-sided materialistic an equally one-sided spiritualistic causal interpretation of culture and history. Each is equally possible, but each if it does not serve as the preparation, but as the conclusion of an investigation, accomplishes equally little in the interest of historical truth." Weber's argument can be understood as an attempt to deepen the understanding of the cultural origins of capitalism, which does not exclude the historical materialist origins described by Marx: modern capitalism emerged from an elective affinity of'material; and 'ideal' factors.

Table of contents.

Table of contents from the 1958 Scribner's edition, with section titles added by Talcott Parsons:<br> Part 1. The Problem  Part 2. The Practical Ethics of the Ascetic Branches of Protestantism.

Criticism.

Methodology.

Weber's causal claim that the Protestant ethic led to capitalism has been criticized for endogeneity problems and case selection problems. Rather than Protestantism leading to capitalism, it may be the case that individuals and communities who were more prone to capitalism were also more likely to adopt Protestantism.

Economic criticism.

The economist and historian Henryk Grossman criticises Weber's analysis on two fronts, firstly with reference to Marx's extensive work which showed that the stringent legal measures taken against poverty and vagabondage was a reaction to the massive population shifts caused by the enclosure of the commons in England. And, secondly, in Grossman's own work showing how this "bloody legislation" against those who had been put off their land was effected across Europe and especially in France. For Grossman this legislation, the outlawing of idleness and the poorhouses they instituted physically forced people from serfdom into wage-labor. For him, this general fact was not related to Protestantism and so capitalism came largely by force and not by any vocational training regarding an inner-worldliness of Protestantism. However, it is possible that the Protestant "work ethic" reinforced or legitimized these legal measures within a larger cultural context.  In a paper published on 10 November 2009, Harvard economist Davide Cantoni tested Weber's Protestant hypothesis using population and economic growth in second-millennium Germany as the data set, with negative results. Cantoni writes:  However, Cantoni uses city size, and not relative real wage growth, which was the Weber thesis, as his "main dependent variable" (Cantoni, 2).  Other recent scholarship continues to find valid Protestant Ethic effects both in historical and contemporary development patterns.  Dudley and Blum write:

Revisionist criticism.

H. M. Robertson, in his book "Aspects of Economic Individualism", argued against the historical and religious claims of Weber. Robertson points out that capitalism began to flourish not in Britain, but in 14th century Italy, a decidedly different epoch. Since this is true, then the rise of capitalism cannot be attributed to Adam Smith, the Protestant Reformation, etc. In fact, Robertson goes further, and states that what happened in Britain was rather a retrogression from what was achieved in Italy centuries earlier.  Looking at the history of the development of economic thought, Robertson shows that Adam Smith and David Ricardo did not found economic science "de novo". In fact, liberal economic theory was developed by French and Italian Catholics, who were influenced by the Scholastics. The British economic thought was rather a step backwards since it espoused the labor theory of value, which had already been proved incorrect by the School of Salamanca.

Other criticism.

Becker and Wossmann of the University of Munich showed that literacy levels differing in religious areas can sufficiently explain the economic gaps cited by Weber. The results were supported even under a concentric diffusion model of Protestantism using distance from Wittenberg as a model.

Support.

In 1958, American sociologist Gerhard Lenski conducted an empirical inquiry into "religion's impact on politics, economics, and family life" in the Detroit, Mich., area. It revealed, among other insights, that there were significant differences between Catholics on the one hand and (white) Protestants and Jews on the other hand with respect to economics and the sciences. Lenski's data supported basic hypotheses of Weber's work "The Protestant Ethic and the Spirit of Capitalism". According to Lenski, "the contribution of Protestantism to material progress have been largely unintended by-products of certain distinctive Protestant traits. This was a central point in Weber's theory." Lenski noted that more than a hundred years prior to Weber, John Wesley, one of the founders of the Methodist church, had observed that "diligence and frugality" made Methodists wealthy. "In an early era, Protestant asceticism and dedication to work, as noted both by Wesley and Weber, seem to have been important patterns of action contributing to economic progress. Both facilitated the accumulation of capital, so critically important to the economic growth and development of nations."  German theologian Friedrich Wilhelm Graf notes: "Sociologists of religion like Peter L. Berger and David Martin have interpreted the Protestant revolution in Latin America as implicit support of basic elements of Weber's thesis. [...] At any rate, many pious persons there interpret their transition from the Roman Catholic church to Protestant Pentecostal congregations in terms of a moral idea that promises long-term economic gains through strong innerworldly asceticism. The strict ascetic self-discipline that has been successfully institutionalized in the Pentecostal congregations, the readiness to work more and with greater effort and to take less leisurely attitudes lead many Pentecostal Christians to believe that their new faith in God is supported by their economic successes."

The Protestant Ethic and the Spirit of Capitalism () is a book written by Max Weber, a German sociologist, economist, and politician. Begun as a series of essays, the original German text was composed in 1904 and 1905, and was translated into English for the first time by American sociologist Talcott Parsons in 1930. It is considered a founding text in economic sociology and a milestone contribution to sociological thought in general.

Protestantská etika a duch kapitalismu (v německém originále Die protestantische Ethik und der Geist des Kapitalismus) je jedno z nejproslulejších děl německého sociologa Maxe Webera. Poprvé bylo toto dílo publikováno v letech 1904–1905. Ačkoliv duch kapitalismu je pojem poprvé použitý Wernerem Sombartem, zásadního významu nabyl až v Protestantské etice a duchu kapitalismu Maxe Webera. Weber se v něm zabývá mimo jiné vztahem mezi rozmachem (nikoli vznikem) kapitalismu a náboženstvím, respektive protestantismem.


Etymology.

The word "aurora" is derived from the name of the Roman goddess of the dawn, Aurora, who travelled from east to

Occurrence.

Most auroras occur in a band known as the "auroral zone", which is typically 3° to 6° wide in latitude and between 10° and 20° from the geomagnetic poles at all local times (or longitudes), most clearly seen at night against a dark sky. A region that currently displays an aurora is called the "auroral oval", a band displaced towards the night side of the Earth. Early evidence for a geomagnetic connection comes from the statistics of auroral observations. Elias Loomis (1860), and later Hermann Fritz (1881) and Sophus Tromholt (1881) in more detail, established that the aurora appeared mainly in the auroral zone. Day-to-day positions of the auroral ovals are posted on the Internet.  In northern latitudes, the effect is known as the aurora borealis or the northern lights. The former term was coined by Galileo in 1619, from the Roman goddess of the dawn and the Greek name for the north wind. The southern counterpart, the aurora australis or the southern lights, has features almost identical to the aurora borealis and changes simultaneously with changes in the northern auroral zone. The aurora australis is visible from high southern latitudes in Antarctica, Chile, Argentina, New Zealand, and Australia.  A geomagnetic storm causes the auroral ovals (north and south) to expand, bringing the aurora to lower latitudes. The instantaneous distribution of auroras ("auroral oval") is slightly different, being centered about 3–5° nightward of the magnetic pole, so that auroral arcs reach furthest toward the equator when the magnetic pole in question is in between the observer and the Sun. The aurora can be seen best at this time, which is called magnetic midnight.  Auroras seen within the auroral oval may be directly overhead, but from farther away, they illuminate the poleward horizon as a greenish glow, or sometimes a faint red, as if the Sun were rising from an unusual direction. Auroras also occur poleward of the auroral zone as either diffuse patches or arcs, which can be subvisual.  Auroras are occasionally seen in latitudes below the auroral zone, when a geomagnetic storm temporarily enlarges the auroral oval. Large geomagnetic storms are most common during the peak of the 11-year sunspot cycle or during the three years after the peak. An electron spirals (gyrates) about a field line at an angle that is determined by its velocity vectors, parallel and perpendicular, respectively, to the local geomagnetic field vector B. This angle is known as the "pitch angle" of the particle. The distance, or radius, of the electron from the field line at any time is known as its Larmor radius. The pitch angle increases as the electron travels to a region of greater field strength nearer to the atmosphere. Thus, it is possible for some particles to return, or mirror, if the angle becomes 90° before entering the atmosphere to collide with the denser molecules there. Other particles that do not mirror enter the atmosphere and contribute to the auroral display over a range of altitudes. Other types of auroras have been observed from space, e.g."poleward arcs" stretching sunward across the polar cap, the related "theta aurora", and "dayside arcs" near noon. These are relatively infrequent and poorly understood. Other interesting effects occur such as flickering aurora, "black aurora" and subvisual red arcs. In addition to all these, a weak glow (often deep red) observed around the two polar cusps, the field lines separating the ones that close through the Earth from those that are swept into the tail and close remotely.

Causes.

A full understanding of the physical processes which lead to different types of auroras is still incomplete, but the basic cause involves the interaction of the solar wind with the Earth's magnetosphere. The varying intensity of the solar wind produces effects of different magnitudes but includes one or more of the following physical scenarios.  The details of these phenomena are not fully understood. However, it is clear that the prime source of auroral particles is the solar wind feeding the magnetosphere, the reservoir containing the radiation zones and temporarily magnetically-trapped particles confined by the geomagnetic field, coupled with particle acceleration processes.

Auroral particles.

The immediate cause of the ionization and excitation of atmospheric constituents leading to auroral emissions was discovered in 1960, when a pioneering rocket flight from Fort Churchill in Canada revealed a flux of electrons entering the atmosphere from above. Since then an extensive collection of measurements has been acquired painstakingly and with steadily improving resolution since the 1960s by many research teams using rockets and satellites to traverse the auroral zone. The main findings have

Auroras and the atmosphere.

Auroras result from emissions of photons in the Earth's upper atmosphere, above, from ionized nitrogen atoms regaining an electron, and oxygen atoms and nitrogen based molecules returning from an excited state to ground state. They are ionized or excited by the collision of particles precipitated into the atmosphere. Both incoming electrons and protons may be involved. Excitation energy is lost within the atmosphere by the emission of a photon, or by collision with another atom or molecule:  Oxygen is unusual in terms of its return to ground state: it can take 0.7 seconds to emit the 557.7 nm green light and up

Auroras and the ionosphere.

Bright auroras are generally associated with Birkeland currents (Schield et al., 1969; Zmuda and Armstrong, 1973), which flow down into the ionosphere on one side of the pole and out on the other. In between, some of the current connects directly through the ionospheric E layer (125 km); the rest ("region 2") detours, leaving again through field lines closer to the equator and closing through the "partial ring current" carried by magnetically trapped plasma. The ionosphere is an ohmic conductor, so some consider that such currents require a driving voltage, which an, as yet unspecified, dynamo mechanism can supply. Electric field

Interaction of the solar wind with Earth.

The Earth is constantly immersed in the solar wind, a rarefied flow of hot plasma (a gas of free electrons and positive ions) emitted by the Sun in all directions, a result of the two-million-degree temperature of the Sun's outermost layer, the corona. The solar wind reaches Earth with a velocity typically around 400 km/s, a density of around 5 ions/cm and a magnetic field intensity of around 2–5 nT (for comparison, Earth's surface field is typically 30,000–50,000 nT). During magnetic storms, in particular, flows can be several times faster; the interplanetary magnetic field (IMF) may also be much stronger. Joan Feynman deduced in the 1970s that the long-term averages of solar wind speed correlated with geomagnetic activity. Her work resulted from data collected by the Explorer 33 spacecraft. The solar wind and magnetosphere consist of plasma (ionized gas), which conducts electricity. It is well known (since Michael Faraday's work around 1830) that when an electrical conductor is placed within a magnetic field while relative motion occurs in a direction that the conductor cuts "across" (or is cut "by"), rather than "along", the lines of the magnetic field, an electric current is induced within the conductor. The strength of the current depends on a) the rate of relative motion, b) the strength of the magnetic field, c) the number of conductors ganged together and d) the distance between the conductor and the magnetic field, while the "direction" of flow is dependent upon the direction of relative motion. Dynamos make use of this basic process ("the dynamo effect"), any and all conductors, solid or otherwise are so affected, including plasmas and other fluids. The IMF originates on the Sun, linked to the sunspots, and its field lines (lines of force) are dragged out by the solar wind. That alone would tend to line them up in the Sun-Earth direction, but the rotation of the Sun angles them at Earth by about 45 degrees forming a spiral in the ecliptic plane), known as the Parker spiral. The field lines passing Earth are therefore usually linked to those near the western edge ("limb") of the visible Sun at any time. The solar wind and the magnetosphere, being two electrically conducting fluids in relative motion, should be able in principle to generate electric currents by dynamo action and impart energy from the flow of the solar wind. However, this process is hampered by the fact that plasmas conduct readily along magnetic field lines, but less readily perpendicular to them. Energy is more effectively transferred by the temporary magnetic connection between the field lines of the solar wind and those of the magnetosphere. Unsurprisingly this process is known as magnetic reconnection. As already mentioned, it happens most readily when the interplanetary field is directed southward, in a similar direction to the geomagnetic field in the inner regions of both the north magnetic pole and south magnetic pole.  Auroras are more frequent and brighter during the intense phase of the solar cycle when coronal mass ejections increase the intensity of the solar wind.

Auroral particle acceleration.

The electrons responsible for the brightest forms of the aurora are well accounted for by their acceleration in the dynamic electric fields of plasma turbulence encountered during precipitation from the magnetosphere into the auroral atmosphere. In contrast, static electric fields are unable to transfer energy to the electrons due to their conservative nature. The electrons and ions that cause the diffuse aurora appear not to be accelerated during precipitation. The increase in strength of magnetic field lines towards the Earth creates a'magnetic mirror' that turns back many of the downward flowing electrons. The bright forms of auroras are produced when downward acceleration not only increases the energy of precipitating electrons but also reduces their pitch angles (angle between electron velocity and the local magnetic field vector). This greatly increases the rate of deposition of energy into the atmosphere, and thereby the rates of ionization, excitation and consequent emission of auroral light. Acceleration also increases the electron current flowing between the atmosphere and magnetosphere.  One early theory proposed for the acceleration of auroral electrons is based on an assumed static, or quasi-static, electric field creating a uni-directional potential drop. No mention is provided of either the necessary space-charge or equipotential distribution, and these remain to be specified for the notion of acceleration by double layers to be credible. Fundamentally, Poisson's equation indicates that there can be no configuration of charge resulting in a net potential drop. Inexplicably though, some authors still invoke quasi-static parallel electric fields as net accelerators of auroral electrons, citing interpretations of

Auroral events of historical significance.

The discovery of a 1770 Japanese diary in 2017 depicting auroras above the ancient Japanese capital of Kyoto suggested that the storm may have been 7% larger than the Carrington event, which affected telegraph networks.  The auroras that resulted from the "great geomagnetic storm" on both 28 August and 2 September 1859, however, are thought to be the most spectacular in recent recorded history. In a paper to the Royal Society on 21 November 1861, Balfour Stewart described both auroral events as documented by a self-recording magnetograph at the Kew Observatory and established the connection between the 2 September 1859 auroral storm and the Carrington-Hodgson flare event when he observed that "It is not impossible to suppose that in this case our luminary was taken "in the act"." The second auroral event, which occurred on 2 September 1859 as a result of the exceptionally intense Carrington-Hodgson white light solar flare on 1 September 1859, produced auroras, so widespread and extraordinarily bright, that they were seen and reported in published scientific measurements, ship logs, and newspapers throughout the United States, Europe, Japan, and Australia. It was reported by "The New York Times" that in Boston on Friday 2 September 1859

Historical theories, superstition and mythology.

An aurora was described by the Greek explorer Pytheas in the 4th century BC. Seneca wrote about auroras in the first book of his "Naturales Quaestiones", classifying them, for instance as "pithaei" ('barrel-like'); "chasmata" ('chasm'); "pogoniae" ('bearded'); "cyparissae" ('like cypress trees'), and describing their manifold colors. He wrote about whether they were above or below the clouds, and recalled that under Tiberius, an aurora formed above the port city of Ostia that was so intense and red that a cohort of the army, stationed nearby for fire duty, galloped to the rescue. It has been suggested that Pliny the Elder depicted the aurora borealis in his "Natural History", when he refers to "trabes", "chasma", 'falling red flames' and 'daylight in the night'.  In Japanese folklore, pheasants were considered messengers from heaven. However, researchers from Japan’s Graduate University for Advanced Studies and National Institute of Polar Research claimed in March 2020 that red pheasant tails witnessed across the night sky over Japan in 620 A.D., might be a red aurora produced during a magnetic storm. In the traditions of Aboriginal Australians, the Aurora Australis is commonly associated with fire. For example, the Gunditjmara people of western Victoria called auroras "puae buae" ('ashes'), while the Gunai people of eastern Victoria perceived auroras as bushfires in the spirit world. The Dieri people of South Australia say that an auroral display is "kootchee", an evil spirit creating a large fire. Similarly, the Ngarrindjeri people of South Australia refer to auroras seen over Kangaroo Island as the campfires of spirits in the 'Land of the Dead'. Aboriginal people in southwest Queensland believe the auroras to be the fires of the "Oola Pikka", ghostly spirits who spoke to the people through auroras. Sacred law forbade anyone except male elders from watching or interpreting the messages of ancestors they believed were transmitted through an aurora.  "Bulfinch's Mythology" relates that in Norse mythology, the armour of the Valkyrior "sheds a strange flickering light, which flashes

Non-terrestrial auroras.

Both Jupiter and Saturn have magnetic fields that are stronger than Earth's (Jupiter's equatorial field strength is 4.3 gauss, compared to 0.3 gauss for Earth), and both have extensive radiation belts. Auroras have been observed on both gas planets, most clearly using the Hubble Space Telescope, and the "Cassini" and "Galileo" spacecraft, as well as on Uranus and Neptune.  The aurorae on Saturn seem, like Earth's, to be powered by the solar wind. However, Jupiter's aurorae are more complex. The Jupiter's main auroral oval is associated with the plasma produced by the volcanic moon, Io and the transport of this plasma within the planet's magnetosphere. An uncertain fraction of Jupiter's aurorae are powered by the solar wind. In addition, the moons, especially Io, are also powerful sources of aurora. These arise from electric currents along field lines ("field aligned currents"), generated by a dynamo mechanism due to the relative motion between the rotating planet and the moving moon. Io, which has active volcanism and an ionosphere, is a particularly strong source, and its currents also generate radio emissions, which have been studied since 1955. Using the Hubble Space Telescope, auroras over Io, Europa and Ganymede have all been observed.  Auroras have also been observed on Venus and Mars. Venus has no magnetic field and so Venusian auroras appear as bright and diffuse patches of varying shape and intensity, sometimes distributed over the full disc of the planet. A Venusian aurora originates when electrons from the solar wind collide with the night-side atmosphere.  An aurora was detected on Mars, on 14 August 2004, by the SPICAM instrument aboard Mars Express. The aurora was located at Terra Cimmeria, in the region of 177° East, 52° South. The total size of the emission region was about 30 km across, and possibly about 8 km high. By analyzing a map of crustal magnetic anomalies compiled with data from Mars Global Surveyor, scientists observed that the region of the emissions corresponded to an area where the strongest magnetic field is localized. This correlation indicated that the origin of the light emission was a flux of electrons moving along the crust magnetic lines and exciting the upper atmosphere of Mars.  The first ever extra-solar auroras were discovered in July 2015 over the brown dwarf star LSR J1835+3259. The mainly red aurora was found to be a million times brighter than the Northern Lights, a result of the charged particles interacting with hydrogen in the atmosphere. It has been speculated that stellar winds may be stripping off material from the surface of the brown dwarf to produce their own electrons. Another possible explanation for the auroras is that an as-yet-undetected body around the dwarf star is throwing off material, as is the case with Jupiter and its moon Io.

An aurora (plural: auroras or aurorae), sometimes referred to as polar lights, northern lights (aurora borealis), or southern lights (aurora australis), is a natural light display in the Earth's sky, predominantly seen in the high-latitude regions (around the Arctic and Antarctic).

Polární záře je souhrnný název pro světelné úkazy nastávající ve vysoké atmosféře ve výškách od 80 do 100 km, nejčastěji kolem 100 km (v ionosféře – oblast vysoké koncentrace iontů a volných elektronů), někdy zasahující i do výšek několika set km. Je to jeden z hlavních jevů vesmírného počasí. Běžně se vyskytují v polárních oblastech (jižní záře – aurora australis, severní záře – aurora borealis), zatímco ve středních zeměpisných šířkách a zejména v tropech jen výjimečně. Jižní a severní záře jsou mírně odlišné.


Climate.

Châteauroux temperatures range from an average January low of to an average August high of.

History.

The old town, close to the river, forms a nucleus around which a newer and more extensive quarter, bordered by boulevards, has grown up; the suburbs of St. Christophe and Déols lie on the right bank of the Indre. The castle from which the city takes its name was built in the latter part of the 10th century by Raoul, prince of Déols. From 920 to 1008, the Norman raids forced the monks of the abbey of Saint-Gildas-de-Rhuys, founded in Brittany by Saint Gildas, to bring his relics to the abbey of Saint-Gildas of Châteauroux that they founded under the protection of the prince Ebbes of Déols, father of Raoul. During the Middle Ages it was the seat of a seigniory, which passed to the Chauvigny from 1207 to 1473 and was raised to the rank of countship in 1497 for Jean V d'Aumont. In 1616, when it was held by Henry II, Prince of Condé, it was raised to the rank of duchy. In 1736 it returned to the crown, and was given to Marie Anne de Mailly-Nesle, duchess of Châteauroux, by Louis XV in 1744. The present Château Raoul housing the "préfecture" offices dates from the 15th century.

Awards.

Châteauroux is one of the communes awarded the grand prize by the Concours National des Villes et Villages Fleuris, a beautification initiative begun in 1959.

Sports.

La Berrichonne de Châteauroux is the town's football club based in Châteauroux, founded in 1883. The team currently plays in Ligue 2, the second division of French football, and played only one season in Ligue 1 in 1997–98. Châteauroux reached the final of the 2003–04 Coupe de France, where they were defeated 1–0 by Paris Saint-Germain, qualifying for the following season's UEFA Cup. The team play their home fixtures at the 17,173-capacity Stade Gaston Petit.

Transport.

There are direct services from Châteauroux railway station to Paris, Orléans, Limoges, Toulouse, and several other regional destinations. The A20 motorway connects Châteauroux with Vierzon, Brive-la-Gaillarde, and Toulouse.  The city offers free public transportation since 2001. Total ridership is up 208% between 2001 and 2012.  The city is served by Châteauroux-Centre "Marcel Dassault" Airport which is in the commune of Déols to the North. The airport is used mainly for cargo, maintenance, training and light aviation but also is served by seasonal charter services.

Personalities.

Born in Châteauroux:

International relations.

Châteauroux is twinned with:

Châteauroux () is the capital of the Indre department in central France and the second-largest town in the province of Berry, after Bourges. Its residents are called "Castelroussins."

Châteauroux ["šatórú"] je město ve Francii, leží v regionu Centre-Val de Loire v départementu Indre, jehož je hlavním městem. Má 44 960 obyvatel (rok 2012), ti se nazývají "Castelroussins". Severně od Châteauroux se nachází letiště Marcela Dassaulta v Déols (IATA: CHR; ICAO: LFLX), které však slouží výhradně nákladní přepravě.


Design and development.

During the spring of 1943, the JNAF issued an 18-Shi specification for a single-seat twin-engine interceptor capable of reaching a top speed of 666 km/h (414 mph) at 6,000 m (19,690 ft). Nakajima submitted a proposal based on the earlier J1N1 "Gekko" three-seat night fighter, although this new aircraft – designated J5N1 – was slightly smaller. The layout of the J5N was similar to the J1N: a low set wing on which were mounted the two powerplants, 1,484 kW (1,990 hp) Nakajima Homare 21 18-cylinder air-cooled radial engines, with a long fuselage ending in a conventional tail arrangement. For maximum utilization of the power from the twin engines, large four-blade propellers were fitted which also featured large spinners (as fitted to the J1N). The main wheels retracted rearwards into the engine nacelles, and the tailwheel was fixed. The cockpit was set above the wing, and featured a starboard-opening canopy. The nose was streamlined to offer the pilot an excellent forward view during landing, takeoff and taxiing.  Armament of the J5N consisted of two 30 mm and two 20 mm cannon, and provision was made for a centreline 250 kg (550 lb) bomb. The J5N was designed to combat the large, heavily armed and fast B-29 Superfortress, and so required such heavy armament in order to do severe damage in the brief windows of time allowed for firing passes. To concentrate the firepower, the four cannons were mounted in the nose of the J5N; if a single-engine fighter were unfortunate enough to find itself in front of a J5N, a single hit from a 30mm shell would have more than adequate to destroy it.

Operational history.

Impressed with the design, the JNAF authorized the development of the J5N1, assigned the name "Tenrai" (天雷"Heavenly Thunder"), and six prototypes were requested to be built. Progress was impeded by the failure of the engines to produce their promised power, and by a steady increase in the weight of the airframe as the need to reverse the long-standing policy of giving low priority to armor protection led to a buildup of weight and a drop in performance. The first prototype – lacking its armament – made its first flight July 13, 1944, and was something of a disappointment. The top speed attained was only 597 km/h (371 mph) – far below the specified 666 km/h (414 mph) of the requirement. Despite the other five prototypes also having flown with numerous enhancements, the aircraft never achieved its design speed, and the project was abandoned soon after in February 1945. Four of the six experimental aircraft were lost to accidents.

The Nakajima J5N was an abandoned Japanese prototype fighter aircraft of the World War II era. J5N was developed as twin-engine interceptor for countering attacks by Boeing B-29 Superfortress.

Nakadžima J5N1 Tenrai (: 天雷, "Tenrai"; : "Hrom") byl dvoumotorový jednomístný stíhací letoun, vyvinutý pro japonské císařské námořní letectvo na sklonku druhé světové války.


History.

RapidShare was founded by Christian Schmid in Mulheim, Germany, initially as "ezShare" later "Rapid Share", a file hosting service for his RapidForum web forum hosting services. In 2004, he started the company RapidShare AG, which went online in August 2004 then moved its premises to Baar, Switzerland in 2006. Schmid avoids the public eye, but took over management of the company after longtime CEO and COO Bobby Chang left in April 2010.  RapidShare's original site was RapidShare.de. Later a second site, RapidShare.com, was started. It operated in parallel with RapidShare.de for several years. On 1 March 2010, RapidShare.de was shut down, and users visiting the site were forwarded to RapidShare.com. Files hosted on RapidShare.de were no longer available for download.  In 2010, RapidShare was said to have hundreds of millions of visitors per month and to be among the 50 most popular Internet sites.  Lawsuits by the owners of copyrighted content shared via RapidShare, and the takedown of file hoster Megaupload, caused RapidShare to revise its business model. The company changed its focus to B2B cloud storage services, but a drop in revenue led to a reduction in staffing by three quarters in May 2013. By 2014 its Alexa ranking had sunk below 1,400.  In late February 2014, the website PCTipp.ch, based on reports from a former RapidShare employee "MarkusP," stated that RapidShare had presented a "quit or be fired" ultimatum to 23 of its 24 employees (already down from 60 employees just two years before) and that most had resigned. The rest, save one, had their contracts terminated. As of mid-March, RapidShare was reported as operating with only one employee, a support person who answered the telephone and managed customers and accounts. The product development team was no more. On 13 March 2014, RapidShare announced price increases for its paid services of about 150%. Free users would continue to be able to use RapidShare, but their download speeds and capacity were sharply curtailed.  On 10 February 2015, RapidShare announced on its home page that it would shut down its services permanently on 31 March 2015. After that date none of the data it hosted would be available, even to the customers who uploaded it. On 31 March 2015, the site home page displayed a notice about the service's closing.

Operation and services.

Upon uploading, the user was supplied with a unique download URL which enabled anyone with whom the uploader shared the URL to download the file. No user was allowed to search RapidShare's servers for content.  In April 2008, RapidShare had 5.4 petabytes of storage for users. In March 2010, it stated, after a 120 Gbit/s upgrade, to have 600 Gbit/s of bandwidth.  Registration and payment allowed benefits such as unlimited download speed, immediate download (instead of experiencing a waiting period), download of several files simultaneously, queue skipping, the facility to interrupt and restart downloads, uploading, downloading bigger files up to 2 GB and to store up to 50 GB of data for an unlimited period.  Until 1 July 2010, RapidShare operated an incentive program that rewarded uploaders with "RapidPoints" according to the number of times those files were downloaded by others; the points were redeemable for premium RapidShare subscriptions. RapidShare discontinued the program to avoid the impression it rewarded its users for uploading copyrighted material.  Downloads by people without a current premium account subscription were subject to restrictions such as an enforced wait of several minutes between downloads. The length of the wait varied over the years, from 15 minutes to over 2.5 hours.

Software.

RapidShare offered two computer programs to simplify file managing:

RapidShare Uploader.

This software allowed queuing of uploads. However, it could not resume interrupted uploads. It was available for Windows and ran without installation.

RapidShare Manager.

This software had many more features than the Uploader, especially queuing and resuming the upload as well as the downloads. The version linked on the site worked with Windows Vista and 7, Mac, and Linux. An older official client was also available for Windows XP.  RapidShare did not restrict automatic downloads to their downloader, however, they did not provide technical support to third-party downloaders as they did for RapidShare Manager.

Legal issues.

On 19 January 2007, the German performance rights organisation GEMA claimed to have won a temporary injunction against both RapidShare.de and RapidShare.com. "The latter is said to have used copyright protected works of GEMA members in an unlawful fashion."  RapidShare started to check newly uploaded files against a database of files already reported as illegal. By comparing the files' MD5-hash the site would now prevent illegal files from being reuploaded. While this would be sufficient under United States law, it was later established in court that under German law it is not. That decision forced RapidShare to check all the uploaded files before publishing them.  In April 2009, RapidShare handed over to major record labels the personal details of uploaders who uploaded copyright-protected files. The incident is reported to have arisen due to a leak of a pre-release copy of metal band Metallica's "Death Magnetic" album.  A month later, RapidShare stated on their website: "we will not spy out the files that our clients faithfully upload onto RapidShare, not now nor in future. We are against upload control and guarantee you that your files are safe with us and will not be opened by anyone else than yourself, unless you distribute the download link."  Six global publishers obtained an injunction against Swiss-based RapidShare AG. Plaintiffs in the case were Bedford, Freeman and Worth Publishing Group, LLC a subsidiary of Macmillan; Cengage Learning Inc.; Elsevier Inc; John Wiley & Sons, Inc.; The McGraw-Hill Companies, Inc.; and Pearson Education, Inc. The judgment handed down by a German court in Hamburg on 10 February 2010, and effective on 17 February 2010, ordered RapidShare to implement measures to prevent illegal file sharing of the 148 copyright-protected works cited in the lawsuit, which was filed on 4 February 2010. The court ruled that RapidShare must monitor its site to ensure the copyrighted material is not being uploaded and prevent unauthorized access to the material by its users. The company will be subject to substantial fines for non-compliance.  The US government's congressional international anti-piracy caucus stated that the site was "overwhelmingly used for the global exchange of illegal movies, music and other copyrighted works".  The Düsseldorf higher regional court twice overturned injunctions filed against RapidShare by Capelight Pictures, a German film and DVD rental company. The court declared that the file hoster could not be held liable for publication of copyright protected material by third parties and revoked the injunction initially upheld by the Düsseldorf district court in the main proceedings. The court also indicated that a file hoster is not obliged to use a word filter as this would also prevent legal copying for private use.  In May 2010, the District Court Southern District of California rejected an injunction against RapidShare filed by the publisher of online erotic magazine Perfect 10. The presiding judge declared that the plaintiff had failed to make a credible case that RapidShare had directly infringed copyright or supported copyright violation.  In a 2009-2010 case brought against RapidShare by Atari Europe, the Düsseldorf higher regional court concluded on appeal that illegal use of RapidShare was by a small minority of its users and that to assume otherwise amounted to "a general suspicion of shared hosting services and their users that cannot be justified". The court also observed that the site removed copyrighted material upon request and did not provide search facilities for illegal material. It concluded that the plaintiff's suggestions for preventing sharing of copyrighted material were "unreasonable or pointless". It also judged that RapidShare could not be held liable for copyright infringements by its users, and that while the service was legal, a minority of illegal use could not be prevented by other measures proposed - for example keyword-based filtering (which could impair legal use), manual review of uploads (not feasible), or IP address analysis (as IP addresses can change frequently).  In December 2010, in response to the congressional international anti-piracy caucus' press release and the German court ruling, RapidShare enlisted the services of Dutko Worldwide to lobby its interests in the United States Congress.  In March 2012, the Hamburg higher regional court upheld three earlier decisions that the file hoster could be held liable for publication of copyright protected material by third parties.  In September 2018, a criminal trial of three Rapidshare managers for commercial assistance to copyright violation is to take place in Zug, Switzerland, where Rapidshare remains incorporated.

RapidShare was an online file hosting service that opened in 2002. In 2009, it was among the Internet's 20 most visited websites and claimed to have 10 petabytes of files uploaded by users with the ability to handle up to three million users simultaneously. Following the takedown of similar service Megaupload in 2012, RapidShare changed its business model to deter the use of its services for distribution of files to large numbers of anonymous users and to focus on personal subscription-only cloud-based file storage. Its popularity fell sharply as a result and, by the end of March 2015, RapidShare ceased to operate and it is defunct.

RapidShare (společnost RapidShare AG Švýcarsko, Cham) byl jeden z největších upload serverů (místo pro nahrání a sdílení souborů) na světě. Hojně využíván hlavně ve světě, i když i v Česku se stal dost populární. Velmi často byl také zneužíván pro sdílení nelegálních souborů a pirátských kopií. Hlavní příjem plynul z prodeje tzv. "Premium" účtů, což je způsob, kdy uživatel může stahovat bez čekání na stažení souboru a dalších omezení. Přesným opakem je "Free" způsob využívání služeb: uživatel se nemusí nijak přihlašovat ani nic platit, ale musí několik desítek sekund počkat na zahájení stahování, rychlost je značně kolísavá a navíc po každém stažení musí 15 minut počkat. Díky této politice mohl RapidShare rozšiřovat své serverové kapacity, aniž by prodělával.


Statement.

Suppose formula_1 and formula_2 are two sequences. Then,  Using the forward difference operator formula_4, it can be stated more succinctly as  Summation by parts is an analogue to integration by parts:  or to Abel's summation formula:  An alternative statement is which is analogous to the integration by parts formula for semimartingales.  Although applications almost always deal with convergence of sequences, the statement is purely algebraic and will work in any field. It will also work when one sequence is in a vector space, and the other is in the relevant field of scalars.

Newton series.

The formula is sometimes given in one of these - slightly different - forms  which represent a special case (formula_10) of the more general rule  both result from iterated application of the initial formula. The auxiliary quantities are Newton series:  and  A particular (formula_15) result is the identity  Here, formula_17 is the binomial coefficient.

Method.

For two given sequences formula_18 and formula_19, with formula_20, one wants to study the sum of the following series:<br> formula_21  If we define formula_22 then for every formula_23 formula_24 and  Finally formula_27  This process, called an Abel transformation, can be used to prove several criteria of convergence for formula_28.

Similarity with an integration by parts.

The formula for an integration by parts is formula_29<br> Beside the boundary conditions, we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( formula_30 becomes formula_31 ) and one which is differentiated ( formula_32 becomes formula_33 ).  The process of the "Abel transformation" is similar, since one of the two initial sequences is summed ( formula_34 becomes formula_35 ) and the other one is differenced ( formula_36 becomes formula_37 ).

Applications.

Proof of Abel's test. Summation by parts gives where "a" is the limit of formula_41. As formula_40 is convergent, formula_46 is bounded independently of formula_47, say by formula_48. As formula_49 go to zero, so go the first two terms. The third term goes to zero by the Cauchy criterion for formula_40. The remaining sum is bounded by  by the monotonicity of formula_41, and also goes to zero as formula_53.  In both cases, the sum of the series satisfies: formula_61

Summation-by-parts operators for high order finite difference methods.

A summation-by-parts (SBP) finite difference operator conventionally consists of a centered difference interior scheme and specific boundary stencils that mimics behaviors of the corresponding integration-by-parts formulation. The boundary conditions are usually imposed by the Simultaneous-Approximation-Term (SAT) technique. The combination of SBP-SAT is a powerful framework for boundary treatment. The method is preferred for well-proven stability for long-time simulation, and high order of accuracy.

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. The summation by parts formula is sometimes called Abel's lemma or Abel transformation.

V matematice je Abelova sumace, pojmenovaná po Nielsi Henriku Abelovi, přepisem n-tého členu posloupnosti na rozdíl dvou po sobě jdoucích členech součtové řady dané touto posloupností.