The Orkneyinga saga is a historical narrative of the history of the Orkney and Shetland islands and their relationship with other local polities Norway and Scotland. The saga has "no parallel in the social and literary record of Scotland" and is "the only medieval chronicle to have Orkney as the central place of action"; the main focus of the work is the line of jarls who ruled the Earldom of Orkney, which constituted the Norðreyjar or Northern Isles of both Orkney and Shetland and there are frequent references to both archipelagoes throughout. The narrative commences with a brief mythical ancestry tale and proceeds to outline the Norse take-over of the Norðreyjar by Harald Fairhair – the former event is not in doubt although the role of the latter King of Norway is no longer accepted by historians as a likelihood; the saga outlines, with varying degrees of detail, the lives and times of the many jarls who ruled the islands between the 9th and 13th centuries. The extent to which the earlier sections in particular can be considered genuine history rather than fiction have been much debated by scholars.

There are several recurring themes in the Orkneyinga saga, including strife between brothers, relationships between the jarls and the Norwegian crown, raiding in the Suðreyjar – the Hebrides. In part, the saga's purpose was to provide a history of the islands and enable its readers to "understand themselves through a knowledge of their origins" but where its historical veracity is lacking it provides modern scholars with insights into the motives of the writers and the politics of 13th century Orkney; this Norse saga was written around in the early thirteenth century by an unknown Icelandic author, associated with the cultural centre at Oddi. Orkneyinga saga belongs to the genre of "Kings’ Sagas" within Icelandic saga literature, a group of histories of the kings of Norway, the best known of, Heimskringla, written by Snorri Sturluson. Indeed Snorri used Orkneyinga saga as one of his sources for Heimskringla, compiled around 1230; as was the case with Icelandic language writing of this period, the aims of the saga were to provide a sense of social continuity through the telling of history combined with an entertaining narrative drive.

The tales are thought to have been compiled from a number of sources, combining family pedigrees, praise poetry and oral legends with historical facts. In the case of the Orkneyinga saga the document outlines the lives of the earls of Orkney and how they came about their earldom. Woolf suggests that the task that the Icelandic compiler was faced with was not dissimilar to trying to write a "history of the Second World War on the basis of Hollywood movies", he notes that a problem with medieval Icelandic historiography in general is the difficulty of fixing of a clear chronology based on stories created in a illiterate society in which "AD dating was unknown" at the time. As the narrative approaches the period closer to the time it was written down, historians have greater confidence in its accuracy. For example, there are significant family connections between Snorri Sturluson and Earl Harald Maddadsson and the original saga document was written down at about the time of Harald's death. Vigfusson identifies several different components to the saga, which may have had different authors and date from different periods.

These are: Fundinn Noregr chapters 1–3 Iarla Sogur chapters 4–38 St Magnus saga chapters 39–55 Iarteina-bok chapter 60 The History of Earl Rognwald and Swain Asleifsson chapters 56–59 and 61–118. A Danish translation dating to 1570 indicates that the original version of the saga ended with the death of Sweyn Asleifsson, killed fighting in Dublin in 1171. Various additions were added circa 1234-5 when a grandson of Asleifsson and a lawmaker called Hrafn visited Iceland; the oldest complete text is found in the late 14th century Flateyjarbók but the first translation into English did not appear until 1873. The first three chapters of the saga are a brief folk legend that sets the scene for events, it commences with characters associated with the elements – Snaer, Logi and Frosti and gives a unique explanation for how Norway came to be named as such, involving Snaer's grandson Nór. There is a reference to claiming land by dragging a boat over a neck of land and the division of the land between Nór and his brother Gór, a recurring theme in the saga.

This legend gives the Orkney jarls an origin involving a giant and king called Fornjót who lived in the far north. This distinguishes them from the Norwegian kings as described in the Ynglingatal and may have been intended to give the jarls a more senior and more Nordic ancestry. Having dealt with the mythical ancestry of the earls, the saga moves on to topics that are intended as genuine history; the next few chapters deal with the creation of the Earldom of Orkney. The saga states that Rognvald Eysteinsson was made the Earl of Møre by the King of Norway, Harald Fairhair. Rognvald accompanied the king on a great military expedition. First the islands of Shetland and Orkney were cleared of vikings, raiding Norway and they continued on to Scotland and the Isle of Man. During this campaign

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. It is a member of a family of notations invented by Paul Bachmann, Edmund Landau, others, collectively called Bachmann–Landau notation or asymptotic notation. In computer science, big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows. In analytic number theory, big O notation is used to express a bound on the difference between an arithmetical function and a better understood approximation. Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation; the letter O is used because the growth rate of a function is referred to as the order of the function. A description of a function in terms of big O notation only provides an upper bound on the growth rate of the function.

Associated with big O notation are several related notations, using the symbols o, Ω, ω, Θ, to describe other kinds of bounds on asymptotic growth rates. Big O notation is used in many other fields to provide similar estimates. Let f be a real or complex valued function and g a real valued function, both defined on some unbounded subset of the real positive numbers, such that g is positive for all large enough values of x. One writes f = O as x → ∞ if and only if for all sufficiently large values of x, the absolute value of f is at most a positive constant multiple of g; that is, f = O if and only if there exists a positive real number M and a real number x0 such that | f | ≤ M g for all x ≥ x 0. In many contexts, the assumption that we are interested in the growth rate as the variable x goes to infinity is left unstated, one writes more that f = O; the notation can be used to describe the behavior of f near some real number a: we say f = O as x → a if and only if there exist positive numbers δ and M such that | f | ≤ M g when 0 < | x − a | < δ.

As g is chosen to be non-zero for values of x sufficiently close to a, both of these definitions can be unified using the limit superior: f = O as x → a if and only if lim sup x → a | f g | < ∞. In typical usage the O notation is asymptotical, that is, it refers to large x. In this setting, the contribution of the terms that grow "most quickly" will make the other ones irrelevant; as a result, the following simplification rules can be applied: If f is a sum of several terms, if there is one with largest growth rate, it can be kept, all others omitted. If f is a product of several factors, any constants can be omitted. For example, let f = 6x4 − 2x3 + 5, suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity; this function is the sum of three terms: 6x4, −2x3, 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of x, namely 6x4. Now one may apply the second rule: 6x4 is a product of 6 and x4 in which the first factor does not depend on x.

Omitting this factor results in the simplified form x4. Thus, we say. Mathematically, we can write f = O. One may confirm this calculation using the formal definition: let f = 6x4 − 2x3 + 5 and g = x4. Applying the formal definition from above, the statement that f = O is equivalent to its expansion, | f | ≤ M x 4 for some suitable choice of x0 and M and for all x > x0. To prove this, let x0 = 1 and M = 13. For all x > x0: | 6 x 4 − 2 x 3 + 5 | ≤ 6 x 4 + |

Yamandu Costa, sometimes misspelled Yamandú, is a Brazilian guitarist and composer. His main instrument is the Brazilian seven-stringed classical guitar. Costa began to study guitar at age seven with his father, Algacir Costa, leader of the group Os Fronteiriços and mastered the instrument after studying with Lúcio Yanel, an Argentine virtuoso who lived in Brazil. At age fifteen, Costa began to study southern Brazilian folk music, as well as the music of Argentina and Uruguay. Influenced by the music of Radamés Gnattali, he began to study the music of other Brazilians, such as Baden Powell de Aquino, Tom Jobim and Raphael Rabello. At age seventeen he played in São Paulo for the first time at the Cultural Circuit Bank of Brazil. Costa's diverse styles include chorinho, bossa nova, tango and chamamé. Costa appeared in Mika Kaurismäki's 2005 documentary film Brasileirinho. Prêmio Tim - Best Soloist - 2004 Winner of the Prêmio Visa, Instrumental edition - 2001 Trophy of Instrumental Music Revelation of the Rio Grande do Sul state 25º Award of Best Instrumentalist of the Rio Grande do Sul state Winner of the Prêmio Califórnia of Uruguaiana - 1995 2020 – Nashville 1996 2018 – Yamandu Costa e Ricardo Herz 2017 – Borghetti Yamandu 2017 – Recanto 2017 – Quebranto 2015 – Lado B 2015 – Tocata à Amizade 2015 – Concerto de Fronteira 2013 – Continente 2011 – Yamandu Costa e Rogério Caetano 2008 – Mafuá 2007 – Lida 2007 – Yamandu + Dominguinhos 2007 – Ida e Volta 2006 – Tokyo Session 2005 – Música do Brasil Vol.

I 2005 – Yamandu Costa ao Vivo 2005 – Brasileirinho 2004 – El Negro Del Blanco 2003 – Yamandu ao Vivo 2001 – Yamandu / Prêmio Visa 2000 – Dois Tempos Official website

L'Arbre de Noël is a 1969 French drama film directed by Terence Young. It was defined as "the most tearful film of sixties"; the film was co-produced by Italy. The story follows a Frenchman named his son Pascal, who live somewhere in France. Along the way, the widower Laurent meets and falls for the beautiful Catherine, but learns that his son is dying after witnessing the explosion of a plane with a nuclear device inside. Finding this out and Pascal have a string of adventures with Catherine along. William Holden as Laurent Ségur Virna Lisi as Catherine Graziani Bourvil as Verdun Brook Fuller as Pascal Ségur Mario Feliciani as Paris doctor Madeleine Damien as Marinette Friedrich von Ledebur as Vernet Georges Douking as Pet owner Jean-Pierre Castaldi as The motorcycle policeman Yves Barsacq as Charlie Lebreton The Christmas Tree on IMDb

North Uist is an island and community in the Outer Hebrides of Scotland. In Donald Munro's A Description of the Western Isles of Scotland Called Hybrides of 1549, North Uist and South Uist are described as one island of Ywst. Starting in the south of this'island', he described the division between South Uist and Benbecula where "the end heirof the sea enters, cuts the countrey be ebbing and flowing through it". Further north of Benbecula he described North Uist as "this countrey is called Kenehnache of Ywst, in Englishe, the north head of Ywst"; some have taken the etymology of Uist from meaning "west", much like Westray in Orkney. Another speculated derivation of Uist from Old Norse is Ívist, derived from vist meaning "an abode, domicile". A Gaelic etymology is possible, with I-fheirste meaning "Crossings-island" or "Fords-island", derived from I meaning "island" and fearsad meaning "estuary, sand-bank, passage across at ebb-tide". Place-names derived from fearsad include Fersit, Belfast. Mac an Tàilleir suggests that a Gaelic derivation of Uist may be "corn island".

However, whilst noting that the -vist ending would have been familiar to speakers of Old Norse as meaning "dwelling", Gammeltoft says the word is "of non-Gaelic origin" and that it reveals itself as one of a number of "foreign place-names having undergone adaptation in Old Norse". A number of standing stones from the Neolithic period are scattered throughout the island, including a stone circle at Pobull Fhinn. In addition to these, a large burial cairn, in pristine condition, is located at Barpa Langass; the island remained inhabited for at least part of the Bronze Age. For the Iron Age, in addition to the wheelhousess typical of the Outer Hebrides, the remains of a broch, from the late Iron Age, can be found at Dun an Sticir. In the 3rd century, stone houses came into use which were shaped like "Jelly Babies". Whoever the occupants of Jelly Baby houses were, they were followed in the 9th century by Viking settlers, who established the Kingdom of the Isles throughout the Hebrides. Vikings built turf-based buildings.

Following Norwegian unification, the Kingdom of the Isles became a crown dependency of the Norwegian king. Malcolm III of Scotland acknowledged in writing that Suðreyjar was not Scottish, king Edgar quitclaimed any residual doubts. However, in the mid-12th century, Somerled, a Norse-Gael of uncertain origin, launched a coup, which made Suðreyjar independent. Following his death, Norwegian authority was nominally restored, but in practice the kingdom was divided between Somerled's heirs, the dynasty that Somerled had deposed; the MacRory, a branch of Somerled's heirs, ruled Uist, as well as Barra, Eigg, Rùm, the Rough Bounds, Bute and northern Jura. In the 13th century, despite Edgar's quitclaim, Scottish forces attempted to conquer parts of Suðreyjar, culminating in the indecisive Battle of Largs. In 1266, the matter was settled by the Treaty of Perth, which transferred the whole of Suðreyjar to Scotland, in exchange for a large sum of money; the Treaty expressly preserved the status of the rulers of Suðreyjar.

At the turn of the century, William I had created the position of Sheriff of Inverness, to be responsible for the Scottish highlands, which theoretically now extended to Garmoran. In 1293, king John Balliol established the Sheriffdom of Skye, which included the Outer Hebrides. Following his usurpation, the Skye sheriffdom ceased to be mentioned, the Garmoran lordship was confirmed to the MacRory leader. In 1343, King David II issued a further charter for this to the latter's son. Just three years the sole surviving MacRory heir was Amy of Garmoran; the southern parts of the Kingdom of the Isles had become the Lordship of the Isles, ruled by the MacDonalds. Amy married the MacDonald leader, John of Islay, but a decade he divorced her, married the king's niece instead; as part of the divorce, John deprived his eldest son, Ranald, of the ability to inherit the Lordship of the Isles, in favour of a son by his new wife. As compensation, John granted Lordship of the Uists to Ranald's younger brother Godfrey, made Ranald Lord of the remainder of Garmoran.

However, on Ranald's death, his sons were still children, Godfrey took the opportunity to seize the Lordship of Garmoran. Furthermore, Godfrey had a younger brother, whose heirs now claimed to own part of North Uist; this led to a great deal of violent conflict involving those of his brothers. Surviving records do not describe this in detail, but traditional accounts report an incident where the Siol Gorrie dug away the embankment of a Loch, causing it to flood a nearby village in which the Siol Murdoch lived. In 1427, frustrated with the level of violence in the highlands, together with the insurrection caused by his own cousin, King James I demanded that highland magnates should attend a meeting at Inverness. On arrival, many of the leaders

The lasing threshold is the lowest excitation level at which a laser's output is dominated by stimulated emission rather than by spontaneous emission. Below the threshold, the laser's output power rises with increasing excitation. Above threshold, the slope of power vs. excitation is orders of magnitude greater. The linewidth of the laser's emission becomes orders of magnitude smaller above the threshold than it is below. Above the threshold, the laser is said to be lasing; the term "lasing" is a back formation from "laser,", an acronym, not an agent noun. The lasing threshold is reached when the optical gain of the laser medium is balanced by the sum of all the losses experienced by light in one round trip of the laser's optical cavity; this can be expressed, assuming steady-state operation, as R 1 R 2 exp ⁡ exp ⁡ = 1. Here R 1 and R 2 are the mirror reflectivities, l is the length of the gain medium, exp ⁡ is the round-trip threshold power gain, exp ⁡ is the round trip power loss. Note that α > 0.

This equation separates the losses in a laser into localised losses due to the mirrors, over which the experimenter has control, distributed losses such as absorption and scattering. The experimenter has little control over the distributed losses; the optical loss is nearly constant for any particular laser close to threshold. Under this assumption the threshold condition can be rearranged as g threshold = α 0 − 1 2 l ln ⁡. Since R 1 R 2 < 1, both terms on the right side are positive, hence both terms increase the required threshold gain parameter. This means that minimising the gain parameter g threshold requires low distributed losses and high reflectivity mirrors; the appearance of l in the denominator suggests that the required threshold gain would be decreased by lengthening the gain medium, but this is not the case. The dependence on l is more complicated because α 0 increases with l due to diffraction losses; the analysis above is predicated on the laser operating in a steady-state at the laser threshold.

However, this is not an assumption which can be satisfied. The problem is that the laser output power varies by orders of magnitude depending on whether the laser is above or below threshold; when close to threshold, the smallest perturbation is able to cause huge swings in the output laser power. The formalism can, however, be used to obtain good measurements of the internal losses of the laser as follows:Most types of laser use one mirror, reflecting, another, reflective. Reflectivities greater than 99.5% are achieved in dielectric mirrors. The analysis can be simplified by taking R 1 = 1; the reflectivity of the output coupler can be denoted R OC. The equation above simplifies to 2 g threshold l = 2 α 0 l − ln ⁡ R OC. In most cases the pumping power required to achieve lasing threshold will be proportional to the left side of the equation, P threshold ∝ 2 g threshold l.. The equation can be rewritten: P threshold = K,where L is defined by L = 2 α 0 l and K is a constant; this relationship allows the variable L to be determined experimentally.

In order to use this expression, a series of slope efficiencies have to be obtained from a laser, with each slope obtained using a different output coupler reflectivity. The power threshold in each case is given by the inte