Plot.

Creation of the mead of poetry and murder of Kvasir.

After the Æsir-Vanir War, the gods sealed the truce they had just concluded by spitting in a vat. To keep a symbol of this truce, they created from their spittle a man named Kvasir. He was so wise that there were no questions he could not answer. He travelled around the world to give knowledge to mankind. One day, he visited the dwarves Fjalar and Galar. They killed him and poured his blood into two vats and a pot called Boðn, Són and Óðrerir. They mixed his blood with honey, thus creating a mead which made anybody who drank it a "poet or scholar" (""skáld eða frœðamaðr""). The dwarves explained to the gods that Kvasir had suffocated in intelligence.

From the dwarves to Suttungr.

Fjalar and Galar invited a giant, Gilling, and his wife. They took him to sea and capsized their boat and the giant drowned. The dwarves then came back home and broke the news to Gilling's wife, which plunged her deep in grief. Fjallar proposed showing her the place where her husband had drowned but Galar got tired of her weeping, went before her and dropped a millstone on her head when she crossed the threshold.  When Gilling's son, Suttungr, learned what had happened, he went to the dwarves and led them to a reef which was covered with water at high tide. The dwarves implored him and offered him the mead in compensation for his father's death. Suttungr agreed. When he came back home, he stored the mead in a place called Hnitbjörg where his daughter, Gunnlöd, was in charge of guarding it.

Theft by Odin.

Odin met nine slaves who were scything hay and offered to sharpen their scythes. His whetstone worked so well that they all wanted to buy it. Odin threw it up in the air and the slaves struggled for it to death, cutting each other's throats.  Then he spent the night at Baugi's place. Baugi was Suttungr's brother. He complained that business did not go well since his slaves had killed each other and he could not get anybody to stand in for them. Odin, who said his name was Bölverk, proposed to do their work in exchange for a draught of Suttungr's mead. Baugi agreed, saying that he would try to persuade his brother. During summer, Bölverk did the work as agreed and, in winter, asked Baugi for his owing. They both went to Suttungr's, who refused to give a single drop of the beverage.  Bölverk then suggested Baugi use a trick. He gave him the drill Rati and asked him to bore into the mountain Hnitbjörg. After Baugi tried to deceive him, a hole was actually dug and Bölverk slipped into it, having taken the form of a snake. Baugi tried in vain to hit him with the drill.  He arrived by Gunnlöd, with whom he spent three nights. Thus he could have three draughts of mead. But with each draught he emptied a whole container. He then transformed into an eagle and flew away. When Suttungr discovered the theft, he too took the shape of an eagle and flew off in hot pursuit. When the Æsir saw Odin coming, they set out vessels in readiness to hold the mead and when, in the nick of time, the god arrived, he spat his loot into them. But Suttungr was so close to him that, in his fear and haste, the god let fall some of the precious liquid from his anus. Anybody could drink of this paltry and sullied portion, which was known as the "rhymester's share" (""skáldfífla hlutr""); but the greater portion of the mead of poetry (which had issued from his mouth) Odin gave to the gods and to those truly gifted in poetry.

Adaptations.

The comic book "The Magic Mead" in the Danish comic book series Valhalla, created by Peter Madsen and others, is a retelling of the story of the mead of poetry. Peter Madsen won The SAS Prize for Best Nordic for this comic at the Raptus Festival in Bergen, Norway.

In Norse mythology, the Poetic Mead or Mead of Poetry, also known as Mead of Suttungr, is a mythical beverage that whoever "drinks becomes a skald or scholar" to recite any information and solve any question. This myth was reported by Snorri Sturluson in Skáldskaparmál. The drink is a vivid metaphor for poetic inspiration, often associated with Odin the god of 'possession' via berserker rage or poetic inspiration.


Snow groomers.

A snowcat dedicated to snow maintenance rather than transport is a snow groomer. Other terms are 'piste machines', 'trail groomers' (in North American English) or 'piste bashers' (in British English) because of their use in preparing ski trails ("pistes") or snowmobile trails.

Other functions.

In addition to grooming snow they are used for polar expeditions, logging in marsh areas, leveling sugar beet piles, and seismic studies in the wild.

Construction.

Most snowcats, such as the ones produced by Bombardier or Aktiv in the past, have two sets of tracks, fitted with a Christie suspension or a Horstmann suspension. Others, like the Tucker Sno-Cat and Hägglunds "Bandvagn 206" vehicles, have a complex arrangement of four or more tracks.  The tracks are usually made of rubber, aluminum or steel and driven by a single sprocket on each side, and ride over rubber wheels with a solid foam interior. Their design is optimized for a snow surface, or soft grounds such as that of a peat bog.  The cabs are optimized for use in sub-zero weather or cold conditions worsened by wind chill, with strong forced heating and a windshield designed to be kept clear of internal and external ice or condensation through a variety of means such as advanced coatings, external scrapers (windshield wipers of a modified type), and internal ducts blowing hot air on the surface.

History.

The forerunners of the snowcat were the tracked "motors" designed by Captain Scott and his engineer Reginald Skelton for the Antarctic Terra Nova Expedition of 1910–1913. These tracked motors were built by the Wolseley Tool and Motor Car Company in Birmingham. In the 1955–1958 Fuchs and Hillary Transantarctic Expedition, four modern snowcats were used, produced by the Tucker Sno-Cat Corporation of Medford, Oregon. These vehicles were highly modified for the purposes of the expedition.  The name "snowcat" originates from the 1946 trademark by Tucker Sno-Cat Corporation. This specialized over-snow vehicle dominated the snow transportation market until the 1960s when other manufacturers entered the business. By then "snowcat" was such a common description that it was used to describe all over-snow vehicles (see generic trademark). Tucker is also well known for its use of four tracks on its vehicles. Tucker Sno-Cat is arguably the best known of the early manufacturers and remains in business today. Tucker Sno-Cats have been used by numerous military, governmental agencies and utilities.  Another early model was the Swedish made Aktiv Snow Trac of which 2265 were manufactured in Sweden between 1957 and 1981. NATO forces used the Snow Trac successfully during the Cold War between NATO and the USSR. Numerous accounts from Antarctica related successful use of the Snow Trac by research organizations such as A.N.A.R.E. in Antarctica.  Thiokol sold its ski-lift and snowcat operation in 1978 to John DeLorean, and changed its name to DeLorean Motor Company (DMC). DMC was later bought out by its management team and renamed Logan Machine Company (LMC). LMC ceased production in 2000. Thiokol's Imp, Super-Imp and Spryte were popular dual-track snowcats and Thiokol's production continued under DMC and LMC. The Spryte, sold later as 1200 and 1500 series machines, are still popular in commercial and industrial use, nearly 20 years after the end of their production runs. Many of these models are still in use today in the commercial market and are popular as privately owned snowcats.  Between 1956 and 1968, KRISTI snowcat had a limited production of two-track snowcats in Colorado; it never became popular and ceased production with fewer than 200 total units produced.  In 1982, Aktiv Snow Trac ceased assembly when its engine supplier (Volkswagen) ceased production of its air-cooled engines in Europe. Over 1000 Snow Tracs were imported to Canada and the United States, mostly by Canadian utilities and U.S. governmental agencies; the Snow Trac is still in common use in private ownership and to a lesser degree in commerce having produced over 2200 total machines which saw popular use all over the globe.

Current production.

Bombardier still continues in business but has radically altered its business model and product selection and sold its snow grooming division and no longer makes commercial snowcats. Bombardier sold over 3000 of its popular snow bus models which are still in use today and in popular demand by dedicated collectors; thousands of other Bombardier models were also produced as ski-slope and snowmobile trail groomers with the Bombi and BR100 to 180 series machines as notable units produced in high quantities. Bombardier Recreational Products still produces the Ski-Doo line of open ridge single-tracked personal snowmobiles.  Russia as one of the snowiest countries in the world has a wide range of snowcat producers, from the big 30-tonnes load capacity two linked tracked Vityaz vehicles to 0.4-2 tonnes load capacity ZZGT vehicles.  The first 100% electric snow groomer was launched by Kässbohrer in June 2019.

A snowcat is an enclosed-cab, truck-sized, fully tracked vehicle designed to move on snow. Major manufacturers are Kässbohrer (Germany), Prinoth (Italy) and Tucker (United States).


Appearance.

The Caucasian Shepherd Dogs is a strongly-boned, muscular, but handsome and even-tempered molossoid dog. Plain dogs have a shorter coat and appear taller as they are less strongly built. Alpine types have a heavier coat and are more muscular.  The Caucasian Ovcharka is a large dog. Minimum weight and height for bitches is /, with a preferred height range of ; for dogs the minimum is /, with a preferred height of.

History.

The Caucasus Mountains are home to many of the oldest living molossoid landrace dogs, such as the Azerbaijani Volkodav, Azerbaijani Shepherd Dog and Georgian Shepherd Dog. During the 20th century the Soviet breeders selected some of these varieties among Caucasian dogs and created the Caucasian Shepherd Dog breed. The modern show class Caucasian Shepherd is a hybrid of established Caucasian types, fundamentally based on the Georgian Shepherd Dog, which is the largest and most muscularly built dog with attractive long hair.  The breed's first official Show-Ring appearance outside the Caucasus was in the 1930s in Germany.  Since ancient times Caucasian mountain dogs have served shepherds in the Caucasus mountains as livestock guardian dogs, defending sheep from predators, mainly wolves, jackals and bears. Caucasian Shepherd Dogs served as guard dogs, bear hunting dogs and today they work as prison guard dogs in Russia.  The Caucasian Shepherd Dog is a fully standardized breed, recognized by major kennel organizations, including the Fédération Cynologique Internationale and the United Kennel Club.  The Caucasian Ovcharka Working Dog Club of America is seeking full recognition from the American Kennel Club.

Temperament.

The Caucasian Shepherd Dog is an extremely independent, self-confident, fearless and intelligent dog. It is a highly protective territorial dog that is wary of unfamiliar people.  It is a low-activity dog, seemingly lethargic when not working, but noisy and intimidating when it feels its family is threatened. Although certain strains are more vicious than others, they are often very territorial and aggressive towards other dogs, needing early and careful broad socialization, as well as consistent, but never forceful, handling. This breed can be a good family-dog, if it is well-trained and socialized.

Health.

The Caucasian Shepherd Dog is generally healthy and long-lived, averaging a life span of 10–12 years. Some dogs may have health problems in the form of hip dysplasia, obesity and occasional heart disorders, but the majority of these dogs are healthy if taken care of correctly. Good dog-breeders use genetic testing of their breeding stock to reduce the chances of diseases in the puppies.  The ears of the Caucasian Shepherd Dog are traditionally cropped, although some modern dogs are unaltered, as many people believe that this practice is unethical and cruel. If brought up by someone with extensive knowledge on the needs of a Caucasian Shepherd Dog, a dog should have much less chance of suffering from bad health.  Exercise and play-time are important to help prevent obesity in this breed. Outdoor activities such as hiking, chasing balls and retrieving flying discs can be a way to keep dogs active and mentally stimulated.

The Caucasian Shepherd Dog (; ; ) is a large livestock guardian dog breed from the Caucasus Mountains, commonly bred in the mountainous regions of Transcaucasia, especially in Georgia.


Biography.

Giraudoux was born in Bellac, Haute-Vienne, where his father, Léger Giraudoux, worked for the Ministry of Transport. Giraudoux studied at the Lycée Lakanal in Sceaux and upon graduation traveled extensively in Europe. After his return to France in 1910, he accepted a position with the Ministry of Foreign Affairs. With the outbreak of World War I, he served with distinction and in 1915 became the first writer ever to be awarded the wartime Legion of Honour.  He married in 1918 and in the subsequent inter-war period produced the majority of his writing. He first achieved literary success through his novels, notably "Siegfried et le Limousin" (1922) and "Eglantine" (1927). An ongoing collaboration with actor and theater director Louis Jouvet, beginning in 1928 with Jouvet's radical streamlining of "Siegfried" for the stage, stimulated his writing. But it is his plays that gained him international renown. He became well known in the English speaking world largely because of the award-winning adaptations of his plays by Christopher Fry ("The Trojan War Will Not Take Place") and Maurice Valency ("The Madwoman of Chaillot", "Ondine", "The Enchanted", "The Apollo of Bellac").  Giraudoux served as a juror with Florence Meyer Blumenthal in awarding the Prix Blumenthal, a grant given between 1919 and 1954 to painters, sculptors, decorators, engravers, writers, and musicians. In politics he was affiliated with the Radical Party, served in the cabinet of Édouard Herriot in 1932, and was appointed as Minister of Information by Édouard Daladier in 1939.  He is buried in the Cimetière de Passy in Paris.

Hippolyte Jean Giraudoux (; 29 October 1882 – 31 January 1944) was a French novelist, essayist, diplomat and playwright. He is considered among the most important French dramatists of the period between World War I and World War II. His work is noted for its stylistic elegance and poetic fantasy. Giraudoux's dominant theme is the relationship between man and woman—or in some cases, between man and some unattainable ideal.


Life.

Rufinus was born in 344 or 345 in the Roman city of Julia Concordia (now Concordia Sagittaria), near Aquileia (in modern-day Italy) at the head of the Adriatic Sea. It appears that both of his parents were Christians.  Around 370, he was living in a monastic community in Aquileia when he met Jerome. In about 372, Rufinus travelled to the eastern Mediterranean, where he studied in Alexandria under Didymus the Blind for some time, and became friends with Macarius the elder and other ascetics in the desert. In Egypt, if not even before leaving Italy, he had become intimately acquainted with Melania the Elder, a wealthy and devout Roman widow. When she moved to Palestine, taking with her a number of clergy and monks on whom the persecutions of the Arian Valens had borne heavily, Rufinus followed her, moving to Jerusalem in 380. There, while his patroness lived in a convent of her own in Jerusalem, Rufinus, at her expense, gathered together a number of monks to form a new monastery on the Mount of Olives, devoting himself to the study of Greek theology. This combination of the contemplative life and the life of learning had already developed in the Egyptian monasteries. When Jerome came to Bethlehem in 386, the friendship formed at Aquileia was renewed. Jerome, along with his patroness Paula, set up a similar community in Bethlehem a few years later. Another of the intimates of Rufinus was John II, Bishop of Jerusalem, and formerly a monk of the Natrun desert, by whom he was ordained to the priesthood in 390.  In 394, as a result of the attacks by Epiphanius of Salamis upon the doctrines of Origen made during a visit to Jerusalem, a fierce quarrel broke out, which found Rufinus and Jerome on different sides. Although both Jerome and Rufinus had previously been great admirers of Origen's work, in the light of Epiphanius' criticism of Origen, Jerome felt that Rufinus was not fierce enough in attacking the works of Origen. Three years afterwards a formal reconciliation was brought about between Jerome and Bishop John, with whom Rufinus sided, but this was to prove only temporary.  In the autumn of 397 Rufinus embarked for Rome, where, finding that the theological controversies of the East were exciting much interest and curiosity, he published a Latin translation of the "Apology of Pamphilus for Origen", and also (398-99) a somewhat free rendering of the "Περὶ Αρχῶν" (or "De Principiis") of that author himself. In the preface to the latter work he referred to Jerome as an admirer of Origen, and as having already translated some of his works with modifications of ambiguous doctrinal expressions. This allusion annoyed Jerome, who was exceedingly sensitive as to his reputation for orthodoxy, and the consequence was a bitter pamphlet war, with Rufinus' "Against Jerome" and Jerome's "Against Rufinus".  At the instigation of Theophilus of Alexandria, Pope Anastasius I (399-401) summoned Rufinus from Aquileia to Rome to vindicate his orthodoxy, but he excused himself from a personal attendance in a written "Apologia pro fide sua". The pope in his reply expressly condemned Origen, but left the question of Rufinus' orthodoxy to his own conscience. He was, however, regarded with suspicion in orthodox circles (cf. the "Decretum Gelasii", 20).  Rufinus spent most of the first decade of the fifth century translating Origen. He translated Origen's homilies for the whole Heptateuch except Deuteronomy, and others on selected Psalms, the Song of Songs, and 1 Samuel. Rufinus' translation of Origen's "Commentary on Romans" (c405-6) gave fresh stimulus to discussions of destiny and free will that had been going on in Roman circles since the mid-390s and would shortly become an issue in Augustine's clash with Pelagius.  Rufinus also translated other works. These include Eusebius' "Ecclesiastical History", translated in 401 at the request of Bishop Chromatius of Aquileia as an antidote to the terror caused by the Gothic incursions into Italy. Rufinus omits much of Eusebius' tenth book, and compresses what remains of it into book 9; he also retouches the narrative in several places and adds two books of his own to bring the account down to the death of Theodosius the Great (395).  Such translations often appear to have been done as a result of a commission, or with a local readership in mind, and so it seems likely that Rufinus worked with the support of friends and patrons. Between 397 and 408 he lived in Italy, probably mainly in Rome and Aquileia; in 408 Rufinus was at the monastery of Pinetum (in the Campagna?), having been driven there by the arrival of Alaric in northern Italy. He fled to Sicily when Alaric moved south and pillaged Rome in 410. He was in the company of Melania the Younger in his flight. He died in Sicily in 411.  Many of his extant works are defences of himself against attacks by Jerome.

Works.

Original works.

The anti-Origenist "Liber de fide" was in the past sometimes attributed to Tyrannius Rufinus, but now it is more often assigned to Rufinus the Syrian.

Translations from Greek to Latin.

Rufinus translated the "Historia Ecclesiastica" of Eusebius of Caesarea and continued the work from the reign of Constantine I to the death of Theodosius I (395). It was published in 402 or 403.  Origen's commentary on the New Testament Epistle to the Romans, along with many of his sermons on the Old Testament, survive only in versions by Rufinus. The full text of Origen's "De principiis" ("On first principals") also survives only in Rufinus' translation. Jerome, earlier a friend of Rufinus, fell out with him and wrote at least three works opposing his opinions and condemning his translations as flawed. For instance, Jerome prepared a (now lost) translation of Origen's "De principiis" to replace Rufinus' translation, which Jerome said was too free.  The other translations of Rufinus are

Quotes from Tyrannius Rufinus.

He said;  "[The Incarnation] was that the divine nature of the Son of God might be like a kind of hook hidden beneath the form of human flesh... to lure on the prince of this world to a contest; that the Son might offer him his human flesh as a bait and that the divinity which lay underneath might catch him and hold him fast with its hook... then, just as a fish when it seizes a baited hook not only fails to drag off the bait but is itself dragged out of the water to serve as food for others; so he that had the power of death sees the body of Jesus in death, unaware of the hook of divinity which lay hidden inside. Having swallowed it, he was immediately caught. The gates of hell were broken, and he was, as it were, drawn up from the pit, to become food for others." — "Christian Theology, an Introduction", Chapter 13, The Doctrine of Salvation in Christ.

Influence.

We can hardly overestimate the influence which Rufinus exerted on Western theologians by thus putting the great Greek fathers into the Latin tongue. Dominic Vallarsi's uncompleted edition of Rufinus (vol. i. folio. Verona, 1745) contains the "De Benedictionibus", the "Apologies", the "Expositio Symboli", the "Historia Eremitica" and the two original books of the "Historia Ecclesiastica". (Vallarsi intended to collect the translations in vol. ii., but it was never published.) See also Migne, "Patrologia Latina" (vol. xxi). For the translations, see the various editions of Origen, Eusebius, etc.

Tyrannius Rufinus, also called Rufinus of Aquileia ("Rufinus Aquileiensis") or Rufinus of Concordia (344/345–411), was a monk, historian, and theologian. He is best known as a translator of Greek patristic material into Latin — especially the work of Origen.


Early life.

Muthesius was born in 1861 in the village of Großneuhausen near Erfurt and received early training from his father, who was a builder. After a period of military service and two years studying philosophy and art history at Frederick William University in Berlin, he enrolled to study architecture at Charlottenburg Technical College in 1883, while also working in the office of Reichstag architect Paul Wallot.

Early career.

Following completion of his studies, Muthesius spent 1887 to 1891 working for German construction firm Ende & Böckmann in Tokyo. There he saw his first building completed—a German Evangelical church in the Gothic Revival style—and was able to travel extensively across Asia. He returned to Germany in 1891 where he worked for the Prussian Ministry of Public Works, studied for a time in Italy on stipend (in 1895), and served for almost two years as the editor of a pair of official construction journals.

London.

In 1896 Muthesius was offered a position as cultural attaché at the German Embassy in London. Muthesius married Anna Trippenbach who was a fashion designer and singer. This gave him the opportunity to study report on the ways of the British. He focused the next six years investigating and residential architecture and domestic lifestyle and design, ending with a three-volume report published in 1904 and 1905 as " ("The English House"), his most famous work. Although his subjects were wide-ranging, he was particularly interested in the philosophy and practices of the English Arts and Crafts movement, whose emphasis on function, modesty, understatement, individuality and honesty to materials he saw as alternatives to the ostentatious historicism and obsession with ornament in German nineteenth century architecture, and whose efforts to bring a sense of craftsmanship to industrial design he saw as a significant national economic benefit. He visited Glasgow to investigate the innovative work of the Glasgow School exemplified by the designs of Charles Rennie Mackintosh, and wrote about houses in Birmingham by William Bidlake.  As well as his official reports, Muthesius also developed a career as an author, communicating his ideas and observations in an influential series of books and articles that saw him become a significant cultural figure in Germany, culminating in ". His wife wrote about Anti-fashion and how she felt that women were being exploited by German clothing industrialists. Her book which incorporated a novel binding designed by Frances MacDonald is considered an important contribution to the Artistic Dress movement.  Muthesius wrote about Glasgow's Willow Tearooms for an issue of "" published in 1905 which was almost entirely devoted to "A Mackintosh Tea Room in Glasgow", saying that "Today any visitor to Glasgow can rest body and soul in Miss Cranston's Tea Rooms and for a few pence drink tea, have breakfast and dream that he is in fairy land." At the same time he lamented Mackintosh's unrewarded struggle to "hold up the banner of Beauty in this dense jungle of ugliness."

Back in Germany.

Muthesius returned to Germany in 1904 and established himself as an architect in private practice, while retaining a role as an official advisor to the Government of focusing his time on reforming art and design education in order that more emphasis be put on workshop training. Over the next two decades he designed a series of houses throughout Germany, drawing upon and cementing the principles and practices expounded in his famous book.

The "Muthesius Affair" and the Deutscher Werkbund.

By this time Muthesius was widely recognised as an admirer of English culture, but this also laid him open to accusations of divided loyalties. In 1907 he was accused by the "Fachverband für die wirtschaftlichen Interessen des Kunstgewerbes" ("Trade Association for the Economic Interests of the Arts and Crafts") of criticising the quality of German industrial products in a lecture in Berlin. The resulting controversy saw several influential designers and industrialists withdraw from the association and set up the "Deutscher Werkbund" ("German Association of Craftsmen"), explicitly aimed at bringing the highest standards of design to mass-produced output.  The Deutscher Werkbund was a major influence on the early careers of Le Corbusier, Walter Gropius and Mies van der Rohe, but although Muthesius was in many ways its spiritual father and served as its chairman from 1910 until 1916, he had little sympathy with the emerging early-modernism, considering both Art Nouveau and the later designs of the Bauhaus to be just as much superficial styles as those of the nineteenth century.  Muthesius was one of the major architects who built Germany's first Garden City, Hellerau, a suburb of Dresden, founded in 1909. Its foundation was closely related with the activities of the Deutscher Werkbund, too. Among the many employees of Muthesius was the German Socialist city planner Martin Wagner, who applied the lessons of the garden city to Berlin on a huge scale, from 1924 to about 1932.

Later career.

Muthesius continued designing houses and writing about domestic architecture until 1927, when he died in a road accident after a site visit in Berlin.

Adam Gottlieb Hermann Muthesius (20 April 1861 – 29 October 1927), known as Hermann Muthesius, was a German architect, author and diplomat, perhaps best known for promoting many of the ideas of the English Arts and Crafts movement within Germany and for his subsequent influence on early pioneers of German architectural modernism such as the Bauhaus.


Indexing.

When dealing with a small number of documents, it is possible for the full-text-search engine to directly scan the contents of the documents with each query, a strategy called "serial scanning". This is what some tools, such as grep, do when searching.  However, when the number of documents to search is potentially large, or the quantity of search queries to perform is substantial, the problem of full-text search is often divided into two tasks: indexing and searching. The indexing stage will scan the text of all the documents and build a list of search terms (often called an index, but more correctly named a concordance). In the search stage, when performing a specific query, only the index is referenced, rather than the text of the original documents.  The indexer will make an entry in the index for each term or word found in a document, and possibly note its relative position within the document. Usually the indexer will ignore stop words (such as "the" and "and") that are both common and insufficiently meaningful to be useful in searching. Some indexers also employ language-specific stemming on the words being indexed. For example, the words "drives", "drove", and "driven" will be recorded in the index under the single concept word "drive".

The precision vs. recall tradeoff.

Recall measures the quantity of relevant results returned by a search, while precision is the measure of the quality of the results returned. Recall is the ratio of relevant results returned to all relevant results. Precision is the number of relevant results returned to the total number of results returned.  The diagram at right represents a low-precision, low-recall search. In the diagram the red and green dots represent the total population of potential search results for a given search. Red dots represent irrelevant results, and green dots represent relevant results. Relevancy is indicated by the proximity of search results to the center of the inner circle. Of all possible results shown, those that were actually returned by the search are shown on a light-blue background. In the example only 1 relevant result of 3 possible relevant results was returned, so the recall is a very low ratio of 1/3, or 33%. The precision for the example is a very low 1/4, or 25%, since only 1 of the 4 results returned was relevant.  Due to the ambiguities of natural language, full-text-search systems typically includes options like stop words to increase precision and stemming to increase recall. Controlled-vocabulary searching also helps alleviate low-precision issues by tagging documents in such a way that ambiguities are eliminated. The trade-off between precision and recall is simple: an increase in precision can lower overall recall, while an increase in recall lowers precision.

False-positive problem.

Full-text searching is likely to retrieve many documents that are not relevant to the "intended" search question. Such documents are called "false positives" (see Type I error). The retrieval of irrelevant documents is often caused by the inherent ambiguity of natural language. In the sample diagram at right, false positives are represented by the irrelevant results (red dots) that were returned by the search (on a light-blue background).  Clustering techniques based on Bayesian algorithms can help reduce false positives. For a search term of "bank", clustering can be used to categorize the document/data universe into "financial institution", "place to sit", "place to store" etc. Depending on the occurrences of words relevant to the categories, search terms or a search result can be placed in one or more of the categories. This technique is being extensively deployed in the e-discovery domain.

Performance improvements.

The deficiencies of free text searching have been addressed in two ways: By providing users with tools that enable them to express their search questions more precisely, and by developing new search algorithms that improve retrieval precision.

Improved search algorithms.

The PageRank algorithm developed by Google gives more prominence to documents to which other Web pages have linked. See Search engine for additional examples.

Software.

The following is a partial list of available software products whose predominant purpose is to perform full-text indexing and searching. Some of these are accompanied with detailed descriptions of their theory of operation or internal algorithms, which can provide additional insight into how full-text search may be accomplished.

In text retrieval, full-text search refers to techniques for searching a single computer-stored document or a collection in a full-text database. Full-text search is distinguished from searches based on metadata or on parts of the original texts represented in databases (such as titles, abstracts, selected sections, or bibliographical references).


Biography.

Scribe was born in Paris and died there. His father was a silk merchant, and he was well educated, being destined for the law. However, he soon began to write for the stage. His first piece, "Le Prétendu sans le savoir", was produced anonymously at the Théâtre des Variétés in 1810 and was a failure. Numerous other plays, written in collaboration with various authors, followed; but Scribe achieved no distinct success till 1815, when he wrote "Une Nuit de la garde nationale" ("Night of the National Guard", 1815), a collaboration with Delestre Poirson. Much of his later work was also written in collaboration with others. His debut in serious comedy was made at the Théâtre Français in 1822 with "Valérie", the first of many successful pieces of the same kind. Among the actors he wrote starring roles for are Mlle Mars and Rachel. Scribe was elected to the Académie Française in 1834.  Scribe's main subject matter was the contemporary bourgeoisie. He mastered his craft writing "comédies vaudevilles", short middle-class entertainments, often with songs. Eventually he developed the formulaic "well-made play"; popular pieces with elaborate plots featuring clever twists and turns, and usually centering on a misunderstanding ("quiproquo") which is revealed early on to the audience but not realised by the protagonists until the final scenes. Characters face a series of obstacles, the resolution of which may create in turn further problems. At the end a "scène a faire", with startling revelations, leads to a sensational denouement. Whilst their ingenuity was recognised by contemporary and later critics, the plays lack fine language, depth of character, thought, or social analysis. They thus stand in sharp contrast, for example, to Romantic plays of the same period, such as those of Victor Hugo. Théophile Gautier questioned how it could be that, "an author without poetry, lyricism, style, philosophy, truth or naturalism could be the most successful writer of his epoch, despite the opposition of literature and the critics?"  Scribe was prolific; he wrote various dramas — vaudevilles, comedies, tragedies and opera libretti. To the Théâtre du Gymnase alone he is said to have furnished a hundred and fifty pieces before 1830. He had a number of co-workers, (Scribe's 'factory'), one of whom supplied the story, another the dialogue, a third the jokes and so on. He is said in some cases to have sent sums of money for "copyright in ideas" to men who were unaware that he had taken suggestions from their work. Among his collaborators were Jean Henri Dupin (1787–1887), Germain Delavigne, Delestre-Poirson, Mélesville, Marc-Antoine Madeleine Désaugiers, Xavier Saintine and Ernest Legouvé.  The mechanical aspect of Scribe's constructions made his works suitable for operatic adaptation, allowing for "effective contrasting of musical treatment, whilst the confrontations provided excellent opportunities for ensembles."  Scribe wrote libretti for operas for many major composers of his time, often for productions destined for the Paris Opéra. Many of these libretti constitute the basis of the Grand Opera genre and changed the whole course of French lyric drama.  He collaborated with Giacomo Meyerbeer on a number of occasions, and also provided the words for works by Giuseppe Verdi ("Les vêpres siciliennes"), Vincenzo Bellini, Daniel Auber ("La muette de Portici", "Gustave III" and others), Fromental Halévy (including "La Juive, Guido et Ginevra", and "Le Juif errant"), François-Adrien Boieldieu, Gaetano Donizetti ("Dom Sébastien") and Gioachino Rossini ("Le comte Ory"). At the time of his death, he was working on a revision of the libretto for Meyerbeer's "L'Africaine", which he had originally written in 1838.  Of his 'historical' operas it has been written: They exist in a parallel universe, in which colourful historical or geographical milieu display a handful of stereotypes who, as a consequence of some secret manoeuvrings in their own pasts and coincidences in the present, are forced to face some implausible crisis of choice or conscience, preferably accompanied by a simultaneous natural disaster or violent death (or both). Scribe's own hard-headed views on his libretti are summarised in his comments on a dispute over payment with Léon Pillet, the director of the Opéra, in 1841: I want to be paid for them according to what they bring in, that is to say, a great deal. The...director only wants to pay for them according to what they are worth, that is to say, very little. Scribe wrote a few novels, but none of any mark. His "Œuvres complètes" appeared in seventy-six volumes between 1874 and 1885.  He has been assumed to be the father of the politician Georges Coulon.

Works.

"See also and "

References.

Notes  Cited sources Other sources

Augustin Eugène Scribe (; 24 December 179120 February 1861) was a French dramatist and librettist. He is known for the perfection of the so-called "well-made play" ("pièce bien faite"), a mainstay of popular theatre for over 100 years, and as the librettist of many of the most successful grand operas.


History.

In 2001, the original Java Specification Request (JSR) for the technology that ultimately became JavaServer Faces proposed developing a package with the name codice_1  By June 2001, "JavaWorld" would report on Amy Fowler's team's design of "the JavaServer Faces API" (aka "Moonwalk") – "an application framework for creating Web-based user interfaces".

How it works.

Based on a component-driven UI design-model, JavaServer Faces uses XML files called view templates or Facelets views. The codice_2 processes requests, loads the appropriate view template, builds a component tree, processes events, and renders the response (typically in the HTML language) to the client. The state of UI components and other objects of scope interest is saved at the end of each request in a process called stateSaving (note: "transient" true), and restored upon next creation of that view. Either the client or the server side can save objects and states.

JSF and Ajax.

JSF is often used together with Ajax, a Rich Internet application development technique. Ajax is a combination of web development techniques and technologies that make it possible to create rich user interfaces. The user interface components in Mojarra (the JSF reference implementation) and Apache MyFaces were originally developed for HTML only, and Ajax had to be added via JavaScript. This has changed, however:  Because JSF supports multiple output formats, Ajax-enabled components can easily be added to enrich JSF-based user interfaces. The JSF 2.0 specification provides built-in support for Ajax by standardizing the Ajax request lifecycle and providing simple development interfaces to Ajax events, allowing any event triggered by the client to go through proper validation, conversion, and finally method invocation, before returning the result to the browser via an XML DOM update.  JSF 2 includes support for graceful degradation when JavaScript is disabled in the browser.

Ajax-enabled components and frameworks.

The following companies and projects offer Ajax-based JSF frameworks or component libraries:

Latest developments.

Facelets (that was designed specifically for JavaServer Faces) was adopted as the official view technology for JSF 2.0. This eliminates the life-cycle conflicts that existed with JSP, forcing workarounds by Java developers. Facelets allows easy component/tag creation using XML markup instead of Java code, the chief complaint against JSF 1.x.  The new JSF developments also provide wide accessibility to Java 5 annotations such as codice_3, codice_4 and codice_5 that removes the need for codice_6 in all cases except framework extension. Navigation has been simplified, removing the need for codice_6 navigation cases. Page transitions can be invoked simply by passing the name of the desired View/Facelet.  Addition of Partial State Saving and DOM updates are part of the built-in standardized Ajax support.  The latest JSF release has built-in support for handling resources like images, CSS and Javascript, allowing artifacts to be included with component libraries, separated into JAR files, or simply co-located into a consistent place within the Web application. This includes logical naming and versioning of resources.  JSF 2.0 also includes a number of other changes like adding support for events, separate development, staging, and production modes, similar to codice_8 in Ruby on Rails, and significantly expanding the standard set of components.

Criticisms.

In their January 2014 "Technology Radar" publication, ThoughtWorks wrote:  In the article published November 2014 in the DZone website, titled "Why You Should Avoid JSF", Jens Schauder wrote:

Rebuttal to criticisms.

In February 2014, Çağatay Çivici (PrimeFaces Lead) responded to ThoughtWorks criticisms in a post titled: JSF is not what you’ve been told anymore. Çivici argues that improvements in JSF over the years offer many features that embrace modern web development, providing the option to write your own JavaScript, HTML, and CSS. Also regarding state, Çağatay wrote:

JavaServer Faces (JSF) is a Java specification for building component-based user interfaces for web applications and was formalized as a standard through the Java Community Process being part of the Java Platform, Enterprise Edition. It is also a MVC web framework that simplifies construction of user interfaces (UI) for server-based applications by using reusable UI components in a page.


Prelude.

From as early as 549 the Emperor Justinian I had planned to dispatch a major army to Italy to conclude the protracted war with the Ostrogoths initiated in 535. During 550-51 a large expeditionary force totaling 20,000 or possibly 25,000 men was gradually assembled at Salona on the Adriatic, comprising regular Byzantine units and a large contingent of foreign allies, notably Lombards, Heruls, and Bulgars. The imperial chamberlain ("cubicularius") Narses was appointed to command in mid 551. The following spring Narses led this Byzantine army around the coast of the Adriatic as far as Ancona, and then turned inland aiming to march down the Via Flaminia to Rome.

Deployment.

At a place known as Busta Gallorum (, lit. "tombs of the Gauls"), near the village of Taginae or Tadinae (traditionally located somewhere to the north of modern Gualdo Tadino), the Byzantines encountered the Ostrogothic army commanded by King Totila, who had been advancing to intercept them. Finding himself considerably outnumbered, Totila ostensibly entered into negotiations while planning a surprise attack, but Narses was not fooled by this stratagem.  Although he enjoyed superiority in numbers, Narses deployed his army in a strong defensive position. In the centre he massed the large body of Germanic mercenaries dismounted in a dense formation and placed the Byzantine troops to either side. On each wing he stationed 4,000 foot-archers.

Battle.

Totila initially attempted to outflank his opponent by seizing a small hill on the Byzantine left which dominated the only route to the rear of the Byzantine line, but some of the Byzantine infantry deployed in a compact well-shielded formation managed to beat off successive attacks of the Ostrogothic cavalry.  Having failed to turn Narses' position, and expecting 2,000 reinforcements from Teia, Totila used various expedients to delay the battle, including disingenuous offers of negotiation and duels enacted between the battle-lines. In one such occasion, Totila sent a Byzantine deserter named Coccas out to challenge any Byzantine to single combat. Coccas was large and immensely strong. He had a reputation among the Goths as a ruthless and powerful fighter. An Armenian named Anzalas, one of Narses' bodyguards, answered the challenge. Coccas charged at Anzalas, but at the last moment, Anzalas swerved his horse and stabbed the Gothic champion in the side. It was not the most auspicious omen for the Ostrogoths.  However, the Ostrogothic king had another delaying tactic. Both armies watched as Totila, dressed in shining purple and gold armor, and riding a huge stallion, cantered out towards the space between the two large armies. His horse went circles, reared, pirouetted, and ran backwards as Totila tossed his lance into the air and caught it. At last, he rode back to his own army and changed into battle armor. Teia had arrived.  His reinforcements having arrived, Totila broke formation and retired for lunch. Narses, wary of a possible ruse, permitted his troops to refresh themselves without leaving their positions. Totila, apparently hoping to take his enemy by surprise, launched a sudden large-scale mounted assault upon the Byzantine center. Ancient and modern authors have accused him of folly, but Totila probably sought to close with the enemy as fast as possible in order to avoid the effects of the formidable Byzantine archers. The Byzantines were prepared for such a move, however, and the archers massed on the flanks to incline their front towards the center so that his battle-line became crescent-shaped. Caught in the enfilading fire from both sides, the Ostrogothic cavalry sustained high casualties and their attack faltered. The course and duration of the subsequent battle are uncertain, but towards early evening Narses ordered a general advance, and the Ostrogoths broke and fled. Although accounts vary, it was probably during the subsequent rout that Totila was killed.

Aftermath.

Narses proceeded to Rome which fell with limited resistance. The Ostrogoths regrouped under Totila's successor Teia, but suffered a final defeat at the Battle of Mons Lactarius (near Mount Vesuvius) and thereafter were most likely absorbed into the Lombards, another Germanic tribe that invaded Italy in the 6th century.

At the Battle of Taginae (also known as the Battle of Busta Gallorum) in June/July 552, the forces of the Byzantine Empire under Narses broke the power of the Ostrogoths in Italy, and paved the way for the temporary Byzantine reconquest of the Italian Peninsula.


Background.

At Tilsit, Napoleon had made an admirer of Alexander, but by the time of the meeting at Erfurt anti-French sentiment at the Russian court was beginning to threaten the newly forged alliance. Napoleon and his foreign minister Jean-Baptiste Nompère de Champagny sought to strengthen the alliance once more in order to settle affairs in Spain and prepare for the expected war with Austria. Working at cross-purposes to Napoleon was Charles Maurice de Talleyrand-Périgord who had by this time come to the conclusion that Napoleon was leading France to destruction, and who secretly advised Alexander to resist Napoleon's demands.

Conference.

The city of Erfurt was under the direct control of the Emperor of the French at this time as Principality of Erfurt. Napoleon attempted to awe Alexander with the glories of the French Empire. The meeting became a great conference involving an array of kings, princes, dukes, barons and notables from all over Europe. Among the attendees was Talma and the entire Comedie Française, who presented sixteen French tragedies over the course of the Congress. Goethe was courted by Napoleon himself and the twenty-year-old Arthur Schopenhauer arrived in Goethe's train and cast a cynical eye over the proceedings.  Out of the meetings came an agreement, the Erfurt Convention, in fourteen articles, calling upon Britain to cease its war against France, recognizing the Russian conquest of Finland from Sweden, and stating that in case of war with Austria, Russia should aid France "to the best of its ability." The two emperors departed for their homelands on 14 October. Six months later the expected war with Austria began, and Alexander barely lived up to his agreement, aiding France as little as possible. By 1810 both emperors were considering war with one another. Erfurt was the last meeting between the two leaders.  By 1812 Russia no longer complied with Napoleon's Continental System of economic warfare against the United Kingdom and anti-French sentiment in the Russian court had reached a new height. Russian defence spending had increased and troops were deployed to the border in preparation for an invasion of Poland. Napoleon pre-empted this by attacking first and with greater force.  From the beginning at Tilsit few onlookers believed these two European powers could peacefully exist side by side, with the Grand Duchy of Warsaw a French satellite state neighbouring Russia. Erfurt may have delayed the eventual outbreak of war, but it was likely the two powers would ultimately come into conflict.

Popular Culture.

The congress is an event referred to by Leo Tolstoy in his "War and Peace" (Book Two Part Three Chapter 1).

The Congress of Erfurt was the meeting between Napoleon, Emperor of the French, and Alexander I, Emperor of All Russia, from Tuesday 27 September to Friday 14 October 1808 intended to reaffirm the alliance concluded the previous year with the Treaties of Tilsit which followed the end of the War of the Fourth Coalition.


Early life.

Meyer was born in Basel, Switzerland, trained as a mason, and practiced as an architect in Switzerland, Belgium, and Germany. From 1916 to 1918 he briefly served as a department manager at the Krupp works in Essen.

Early work.

Between 1919 and 1921 Meyer completed planning the housing estate "Freidorf" near the Swiss city of Basel.  In 1923 Meyer co-initiated the architectural magazine 'ABC Beiträge zum Bauen' (Contributions on Building) with Hans Schmidt, Mart Stam, and the Suprematist El Lissitzky in Zurich.  Meyer's design philosophy is represented by the quote following:  "1. sex life, 2. sleeping habits, 3. pets, 4. gardening, 5. personal hygiene, 6. weather protection, 7. hygiene in the home, 8. car maintenance, 9. cooking, 10. heating, 11. exposure to the sun, 12. services - these are the only motives when building a house. We examine the daily routine of everyone who lives in the house and this gives us the functional diagram - the functional diagram and the economic programme are the determining principles of the building project."(Meyer, 1928) In 1926 Meyer established a company with Hans Wittwer and produced his two most famous designs, for the Basel Petersschule (1926) and for the Geneva League of Nations Building (1926/1927). Both projects are strict, inventive, and rely on the new possibilities of structural steel. Neither was built. The Petersschule was designed to be a new primary school for girls, such that the school itself would be raised as high above the ground as possible to allow for sunlight and fresh air.

Bauhaus.

Walter Gropius appointed Meyer director of the Bauhaus architecture department when it was finally established during April 1927, though Mart Stam had been Gropius's first choice. Meyer brought his radical functionalist philosophy which he named, during 1929, "Die neue Baulehre" (the new way to build). His philosophy was that architecture was an organizational task without relationship to aesthetics, that buildings should be low cost and designed to fulfill social needs. He was dismissed for allegedly politicizing the school.  Meyer brought the two most significant building commissions for the school, both of which still exist: five apartment buildings in the city of Dessau known as "Laubenganghäuser" ("Houses with Balcony Access"). The apartments are considered to be'real' Bauhaus buildings because they originated with the Bauhaus department of Architecture. The development bordered on the Törten housing estate which was designed by Walter Gropius.  The other major building commission was the Bundesschule des Allgemeinen Deutschen Gewerkschaftsbundes (ADGB Trade Union School), in Bernau bei Berlin, which was completed during 1930. It was the second largest project ever undertaken by the Bauhaus, after the Bauhaus school buildings in Dessau. The school operated for only three years until the Nazis confiscated it during 1933 for use as a management training school. The building now has historic protection status and it experienced an extensive restoration which was completed during 2007. The restoration project won the World Monuments Fund / Knoll Modernism prize during 2008.  In July 2017 both the Laubenganghäuser and the ADGB Trade Union School were inscribed as part of the Bauhaus and its Sites in Weimar, Dessau and Bernau World Heritage Site.  Walter Gropius appointed Meyer to replace him as the school's director on 1 April 1928. Meyer continued with Gropius' innovations to emphasize designing prototypes for serial mass production and functionalist architecture. In the increasingly dangerous political era of the Weimar Republic, Dessau's Mayor, Hesse, alleged that Meyer allowed a Communist student organization to flourish and bring bad publicity to the school, threatening its survival. Hesse dismissed Meyer as head of the Bauhaus school, with a monetary settlement, on August 1, 1930. Meyer's open letter in a left-wing newspaper two weeks later characterizes the Bauhaus as "Incestuous theories (blocking) all access to healthy, life-oriented design... As head of the Bauhaus, I fought the Bauhaus style".

After Bauhaus.

In the autumn of 1930, Meyer emigrated to the USSR along with several former Bauhaus students, including Konrad Püschel and. He taught at WASI, a Soviet academy for architecture and civil engineering. During his years in the Soviet Union, he acted as an advisor for urban projects at Giprogor (the Soviet Institute for Urban and Investment Development) and created plans related to aspects of the redevelopment of Moscow as part of the first five-year plan.  Outside of Moscow Meyer realised his ideas especially in the recently created Jewish Autonomous Oblast in the far east of the USSR. Meyer realized not only the buildings (such as worker's dormitory, theatre etc.), and their internal design and furnishings, but also developed the urbanist project for the area's capital, the city of Birobidzhan.  In 1936 Meyer relocated to Geneva for three years, then emigrated to Mexico City to work for the Mexican government as the director of the Instituto del Urbanismo y Planificación from 1939 through 1941. In 1942, he became the director of Estampa Mexicana, the publishing house of the Taller de Gráfica Popular (the Popular Graphic Arts Workshop).  Meyer returned to Switzerland in 1949 and died in 1954.

Hans Emil "Hannes" Meyer (November 18, 1889 – July 19, 1954) was a Swiss architect and second director of the Bauhaus Dessau from 1928 to 1930.


History.

It is believed that the Stanegate was probably built under the governorship of Agricola, from 77 to 85 AD, during the reigns of the emperors Vespasian, Titus and Domitian. It is also thought that it was built as a strategic road when the northern frontier was on the line of the Forth and Clyde, and only later became part of the frontier when the Romans withdrew from what is now Scotland. An indication of this is that it was provided with forts at one-day marching intervals (14 Roman miles or modern ), sufficient for a strategic non-frontier road. The forts at Vindolanda (Chesterholm) and Nether Denton have been shown to date from about the same time as Corstopitum and Luguvalium, in the 70s AD and 80s AD. When the Romans decided to withdraw from Scotland, the line of the Stanegate became the new frontier and it became necessary to provide forts at half-day marching intervals. These additional forts were Newbrough, Magnis (Carvoran) and Brampton Old Church. It has been suggested that a series of smaller forts were built in between the 'half-day-march' forts. Haltwhistle Burn and Throp might be such forts, but there is insufficient evidence to confirm a series of such fortlets. The retreat from Scotland took place in about 105 AD, and so the strengthening of the Stanegate defences would date from about that time.

Structure.

Where it left the base of Corstopitum, the Stanegate was wide with covered stone gutters and a foundation of cobbles with of gravel on top.

Route.

The Stanegate began in the east at Corstopitum, where the important road, Dere Street headed towards Scotland. West of Corstopitum, the Stanegate crossed the Cor Burn, and then followed the north bank of the Tyne until it reached the North Tyne near the village of Wall. A Roman bridge must have taken the road across the North Tyne, from where it headed west past the present village of Fourstones to Newbrough, where the first fort is situated, from Corbridge, and from Vindolanda. It is a small fort occupying less than an acre and is in the graveyard of Newbrough church, which stands alone to the west of the village.  From Newbrough, the Stanegate proceeds west, parallel to the South Tyne until it meets the next major fort, at Vindolanda (Chesterholm). From Vindolanda the Stanegate crosses the route of the present-day Military Road and passes just south of the minor fort of Haltwhistle Burn. From Haltwhistle Burn, the Stanegate continues west away from the course of the South Tyne and passes the major fort of Magnis (Carvoran), from Vindolanda and from Corstopitum. At this point, the road is joined by the Maiden Way coming from Epiacum (Whitley Castle) to the south.  From Magnis, the road turns towards the southwest to follow the course of the River Irthing, passing the minor fort of Throp, and arriving at the major fort of Nether Denton, from Magnis and from Corstopitum. The fort occupies an area of about.  From Nether Denton, the road continues to follow the River Irthing and heads towards present-day Brampton. It passes the minor fort of Castle Hill Boothby and then, west of Brampton, reaches the next major fort, that of Brampton Old Church, from Nether Denton and from Corstopitum. The fort is so called because half of it is buried under Old St Martin's church and its graveyard.  From Brampton Old Church, the road crosses the River Irthing and continues southwest through Irthington and passes through what is now the site of Carlisle Airport, just to the north of the main runway. The curving corner of an associated marching camp can be made out from the air on the south edge of the runway near its western end, and can be seen on Google Earth. The Stanegate then continued through a large cutting in High Crosby, where a small fort has been postulated, based on marching distances, but has not yet been found. The Stanegate then crossed the River Eden near the cricket ground in modern Carlisle and eventually reached the fort of Luguvalium (Carlisle) on the site of Carlisle Castle, from Brampton Old Church and from Corstopitum. It has been suggested that the road may have carried on west for a further to the Roman fort at Kirkbride overlooking Moricambe Bay, an inlet of the Solway Firth. A large camp of was found there but the evidence for a road is insufficient.  It has also been suggested that the Stanegate may have run eastwards from Corstopitum towards Pons Aelius, present-day Newcastle upon Tyne, and possibly linking to Washing Wells Roman Fort in Whickham, but no evidence has yet been found to support this.

Subsequent history.

Much of the Stanegate provided the foundation for the Carelgate (or Carlisle Road), a medieval road running from Corbridge market place and joining the Stanegate west of Corstopitum. The Carelgate eventually deteriorated to such an extent that it was unusable by coaches and wagons. In 1751–1752, a new Military Road was built by General George Wade in the wake of the Jacobite rising of 1745.

The Stanegate (meaning "stone gate" or "stone road" in Northumbrian dialect ), was an important Roman road built in what is now northern England. It linked two forts that guarded important river crossings: Corstopitum (Corbridge) on the River Tyne in the east, and situated on Dere Street, and Luguvalium (Carlisle) on the River Eden in the west. The Stanegate ran through the natural gap formed by the valleys of the River Tyne in Northumberland and the River Irthing in Cumbria. It predated Hadrian's Wall by several decades; the Wall would later follow a similar route, slightly to the north.


Definitions.

Various groups use different definitions to identify orphans. One legal definition used in the United States is a minor bereft through "death or disappearance of, abandonment or desertion by, or separation or loss from, both parents".  In the common use, an orphan does not have any surviving parent to care for them. However, the United Nations Children's Fund (UNICEF), Joint United Nations Programme on HIV and AIDS (UNAIDS), and other groups label any child who has lost one parent as an orphan. In this approach, a "maternal orphan" is a child whose mother has died, a "paternal orphan" is a child whose father has died, and a "double orphan" is a child/teen/infant who has lost both parents. This contrasts with the older use of "half-orphan" to describe children who had lost only one parent.

Populations.

Orphans are relatively rare in developed countries, because most children can expect both of their parents to survive their childhood. Much higher numbers of orphans exist in war-torn nations such as Afghanistan.

Notable orphans.

Famous orphans include world leaders such as Nelson Mandela, Alexander Hamilton, Kayleigh Chalk, Aaron Burr, Andrew Jackson; the Hebrew prophet Moses and the Muslim prophet Muhammad; writers such as Edgar Allan Poe, and Leo Tolstoy; athletes such as Aaron Hernandez and Jacques Villeneuve. The American orphan Henry Darger portrayed the horrible conditions of his orphanage in his art work. Other notable orphans include entertainment greats such as Louis Armstrong, Marilyn Monroe, Babe Ruth, Ray Charles and Frances McDormand, and innumerable fictional characters in literature and comics.

History.

Wars and great epidemics, such as AIDS, have created many orphans. The Second World War, with its massive numbers of deaths and population movements, created large numbers of orphans in many countries—with estimates for Europe ranging from 1,000,000 to 13,000,000. Judt (2006) estimates there were 9,000 orphaned children in Czechoslovakia, 60,000 in the Netherlands 300,000 in Poland and 200,000 in Yugoslavia, plus many more in the Soviet Union, Germany, Italy and elsewhere.

In literature.

Orphaned characters are extremely common as literary protagonists, especially in children's and fantasy literature. The lack of parents leaves the characters to pursue more interesting and adventurous lives, by freeing them from familial obligations and controls, and depriving them of more prosaic lives. It creates characters that are self-contained and introspective and who strive for affection. Orphans can metaphorically search for self-understanding through attempting to know their roots. Parents can also be allies and sources of aid for children, and removing the parents makes the character's difficulties more severe. Parents, furthermore, can be irrelevant to the theme a writer is trying to develop, and orphaning the character frees the writer from the necessity to depict such an irrelevant relationship; if one parent-child relationship is important, removing the other parent prevents complicating the necessary relationship. All these characteristics make orphans attractive characters for authors.  Orphans are common in fairy tales, such as most variants of "Cinderella".  A number of well-known authors have written books featuring orphans. Examples from classic literature include Charlotte Brontë's "Jane Eyre", Charles Dickens's "Oliver Twist", Mark Twain's "Tom Sawyer", L. M. Montgomery's "Anne of Green Gables", Thomas Hardy's "Jude the Obscure", and J. R. R. Tolkien's "The Lord of the Rings". Among more recent authors, A. J. Cronin, Lemony Snicket, A. F. Coniglio, Roald Dahl and J. K. Rowling, as well as some less well-known authors of famous orphans like Little Orphan Annie have used orphans as major characters. One recurring storyline has been the relationship that the orphan can have with an adult from outside their immediate family as seen in Lyle Kessler's play "Orphans".  Orphans are especially common as characters in comic books. Almost all the most popular heroes are orphans: Superman, Batman, Spider-Man, Robin, The Flash, Captain Marvel, Captain America, and Green Arrow were all orphaned. Orphans are also very common among villains: Bane, Catwoman, and Magneto are examples. Lex Luthor, Deadpool, and Carnage can also be included on this list, though they killed one or both of their parents. Supporting characters befriended by the heroes are also often orphans, including the Newsboy Legion and Rick Jones.

Cartoons.

All of the orphan children from the 1936 "Color Classic", "Christmas Comes But Once a Year" produced by Fleischer Studios, were voiced by Mae Questel.

In religious texts.

Many religious texts, including the Bible and the Quran, contain the idea that helping and defending orphans is a very important and God-pleasing matter. The religious leaders Moses and Muhammad were orphaned as children. Several scriptural citations describe how orphans should be treated:  Bible  Qu'ran

An orphan (from the ) is a child whose parents have died, are unknown, or have permanently abandoned them. In common usage, only a child who has lost both parents due to death is called an orphan. When referring to animals, only the mother's condition is usually relevant (i.e. if the female parent has gone, the offspring is an orphan, regardless of the father's condition).


Formation.

Scientific studies suggest that Lake Tai's circular structure is the result of a meteor impact based on the discovery of shatter cones, shock-metamorphosed quartz, microtektites, and shock-metamorphic unloading fractures. The prospective impact crater has been dated to be greater than 70 million years old and possibly from the late Devonian Period. However, new research suggests that present evidence shows no impact crater structure or shock-mineral at Lake Tai. Fossils indicate that Lake Tai was dry land until the ingression of the East China Sea during the Holocene epoch. The growing deltas of the Yangtze and Qiantang rivers eventually sealed off Lake Tai from the sea, and the influx of fresh water from rivers and rains turned it into a freshwater lake.

Scenic locations.

The lake is renowned for its unique limestone formations at the foot of the adjacent Dongting Mountain (). These "scholar's rocks" or "Taihu stones" are often prized as a decorating material for traditional Chinese gardens, as exemplified by those preserved as museums in nearby Suzhou.  Lake Tai is best seen from atop the Dragon Light Pagoda in western Wuxi's Xihui Park, from which both Wuxi and Lake Tai are visible. Another well-known panoramic view, made famous by an 11th-century poem by Su Shi, is that from Longshan.  Three of the lake's islands are preserved as a national geological park under the name Sanshan. They are famed as a former haunt of local bandits. Mei Yuan is also located in Lake Tai, along with Yuantouzhu. Yuantouzhu received its name ("Turtle Head Isle") from the shape of its outline.

Ferris wheel.

The "Star of Lake Tai" is a giant, Ferris wheel on the shore of the lake. Completed in 2008, it takes 18 minutes to complete one revolution. Passengers can enjoy the scenery of Lake Tai and the city center. At night, lighting effects are switched on around the wheel.

Business and industry.

The lake is known for its productive fishing industry and is often covered by fleets of small private fishing boats. Since the late 1970s, harvesting food products such as fish and crabs has been invaluable to people living along the lake and has contributed significantly to the economy of the surrounding area.  The lake is home to an extensive ceramic industry, including the Yixing pottery factory, which produces world-renowned Yixing clay teapots.

Pollution.

Pollution of the lake has been ongoing for decades despite efforts to reduce pollution that were not sustained and thus proved ineffective. In the 1980s and 1990s, the number of industries in the lake region tripled, and the population also increased significantly. One billion tons of wastewater, 450,000 tons of garbage, and 880,000 tons of animal waste were dumped into the shallow lake in 1993 alone. The central government intervened and initiated a campaign to clean up the lake, setting a deadline to comply with pollution standards. When the deadline was not met, 128 factories were closed on New Year's Eve in 1999. Compliance improved somewhat afterwards, but the pollution problem remained severe.  In May 2007, the lake was overtaken by a major algae bloom and by major pollution with cyanobacteria. The Chinese government called the lake a major natural disaster despite the anthropogenic origin of this environmental catastrophe. With the average price of bottled water rising to six times the normal rate, the government banned all regional water providers from implementing price hikes. (The lake provides water to 30 million residents, including about one million in Wuxi.) By October 2007, it was reported that the Chinese government had shut down or given notice to over 1,300 factories around the lake. Nonetheless, Wu Lihong, one of the leading environmentalists who had been publicizing pollution of the lake, was sentenced to three years in prison for alleged extortion of one of the polluters, but, undeterred, alleged in 2010 that not a single factory was closed.  Jiangsu province planned to clean the lake; chaired by Wen Jiabao, the State Council set a target to complete the task by 2012. However, in 2010 "The Economist" reported that pollution had broken out again and that Wu Lihong, released from prison that April, was claiming that the government was trying to suppress news of the outbreak while switching to other supplies in place of lake water.

Taihu (), also known as Lake Tai or Lake Taihu, is a lake in the Yangtze Delta and one of the largest freshwater lakes in China. The lake lies in Jiangsu province and significant part of its southern shore forms its border with Zhejiang. With an area of and an average depth of, it is the third-largest freshwater lake entirely in China, after Poyang and Dongting. The lake holds about 90 islands, ranging in size from a few square meters to several square kilometers.


Attitude.

Animal supporters are, by default, as close to rampant as possible, if the nature of the supporter allows it (this does not need to be mentioned in the blazon), though there are some blazoned exceptions. An example of whales 'non-rampant' is the arms of the Dutch municipality of Zaanstad.

Regional development and entitlement.

Older writers trace origins of supporters to their usages in tournaments, where the shields of the combatants were exposed for inspection, and guarded by their servants or pages disguised in fanciful attire. However, medieval Scottish seals afford numerous examples in which the 13th and 14th century shields were placed between two creatures resembling lizards or dragons. Also, the seal of John, Duke of Normandy, eldest son of the King of France, before 1316 bears his arms as; France ancient, a bordure "gules", between two lions rampant away from the shield, and an eagle with expanded wings standing above it.

Canada.

In Canada, Companions of the Order of Canada, Commanders of the Order of Military Merit, Commanders of the Royal Victorian Order: people granted the style the Right Honourable, and corporations are granted the use of supporters on their coats of arms. Further, on his retirement from office as Chief Herald, Robert Watt was granted supporters as an honour.

France.

In France, writers made a distinctive difference on the subject of supporters, giving the name of "Supports" to animals, real or imaginary, thus employed; while human figures or angels similarly used are called "Tenants" (i.e. 'holders'). Trees and other inanimate objects which are sometimes used are called "Soutiens".

New Zealand.

Knights Grand Companion and Principal Companions of the New Zealand Order of Merit are granted the use of heraldic supporters.

United Kingdom.

Originally, in England, supporters were regarded as little more than mere decorative and artistic appendages.  In the United Kingdom, supporters are typically an example of special royal favour, granted at the behest of the sovereign. Hereditary supporters are normally limited to hereditary peers, certain members of the Royal Family, and to some chiefs of Scottish clans. Non-hereditary supporters are granted to life peers, Knights and Ladies of the Order of the Garter and Order of the Thistle, Knights and Dames Grand Cross of the Order of the Bath, Order of St Michael and St George, Royal Victorian Order and Order of the British Empire, and Bailiffs and Dames Grand Cross of the Order of St John. Knights banneret were also granted non-hereditary supporters, but no such knight has been created since the time of Charles I.  Supporters may also be granted to corporations which have a royal charter.

USS "Iowa" (BB-61) is a retired battleship, the lead ship of her class, and the fourth in the United States Navy to be named after the state of Iowa. Owing to the cancellation of the s, "Iowa" is the last lead ship of any class of United States battleships and was the only ship of her class to have served in the Atlantic Ocean during World War II.


Etymology.

The resemblance of the foliage to that of the common European holly, "Ilex aquifolium", has led to its common and botanic names. The name "" was originally the classical Latin name for the holm oak, but later adopted as a botanical genus name for the hollies.

Description.

An evergreen tree of large size, attaining in favourable places a height of 21–28 m, and developing in open situations a huge head of densely leafy branches as much across, the terminal portions of the branches usually pendulous in old trees. The trunk is sometimes over 6 m in girth. The young shoots are clothed with a close grey felt. The leaves are very variable in shape, most frequently narrowly oval or ovate-lanceolate, 4–8 cm long, 1.2–2.5 cm wide, rounded or broadly tapered at the base, pointed, the margins sometimes entire, sometimes (especially on young trees) more or less remotely toothed. When quite young, both surfaces are clothed with whitish down, which soon falls away entirely from the upper surface leaving it a dark glossy green; on the lower surface it turns grey or tawny, and persists until the fall of the leaf; the petiole is 3–16 mm long. Fruits are produced one to three together on a short downy stalk, ripening the first season; the acorns usually 12–18 mm long in the UK, the cups with appressed, downy scales.

Subspecies.

There are two subspecies:

Ecology.

Holm oak grows in pure stands or mixed forest in the Mediterranean and often at low or moderate elevations. One of the plant associations in which holm oak is found is the holm oak/Atlas cedar forests of the Atlas Mountains. In Morocco, some of these mixed forests are habitat to the endangered primate, Barbary macaque, "Macaca sylvanus".  Holm oak is prevalent from Portugal to Greece along the northern Mediterranean coastal belt, and from Morocco to Tunisia along the southern Mediterranean coast.  Holm oak is damaging biodiversity in the United Kingdom and is listed as an alien invader. Normally the tree is unable to withstand severe frost, which would prevent it from spreading north, but with climate change, it has successfully penetrated and established itself in areas north of its native range. The largest population of Holm oak in Northern Europe is present on and around St. Boniface Down on the Isle of Wight and into the neighbouring town of Ventnor, a town known for its naturally warmer microclimate, and has shown to tolerate the high winds on the downs. It is thought that this population's propagation (which was established in the late 1800s after having been planted by Victorian residents) has been bolstered by native Eurasian jays ("Garrulus glandarius"), which harvest acorns from oak trees and store them by burying them in the ground where they may then germinate.

Cultivation and uses.

The wood is hard and tough, and has been used since ancient times for general construction purposes as pillars, tools, wagons (Hesiod, "Works and Days" 429), vessels and wine casks. It is also used as firewood and in charcoal manufacture.  The holm oak is one of the top three trees used in the establishment of truffle orchards, or truffières. Truffles grow in an ectomycorrhizal association with the tree's roots.  The acorns, like those of the cork oak, are edible (toasted or as a flour) and are an important food for free-range pigs reared for ibérico ham production. Boiled in water, the acorns can also be used as a medicinal treatment for wound disinfections.  "Q. ilex" can be clipped to form a tall hedge, and it is suitable for coastal windbreaks, in any well drained soil. It forms a picturesque rounded head, with pendulous low-hanging branches. Its size and solid evergreen character gives it an imposing architectural presence that makes it valuable in many urban and garden settings. While holm oak can be grown in much of maritime northwestern Europe, it is not tolerant of cold continental winters.

Notable trees.

The TROBI Champion in Gloucestershire measured in circumference at 1.2 m height in 1993. Another tree at Courtown House, Wexford, Ireland, reputedly planted in 1648, measured 20 m in height, with a spread of 43 m in 2010.An ancient tree reputed to be 500 years old at Fulham Palace, London is listed as one of the Great Trees of London.  The oldest holm oak in Spain, the Encina Tres Patas de Mendaza, located in Navarre, is reputed to be 1,200 years old. A specimen in Milo, in Sicily, is reputed to be 700 years old while a small population on the slopes of northern village of Wardija in Malta are said to be between 500 and 1,000 years old. Prior to the Carthaginian period, holm oak was prevalent on the islands.

Quercus ilex, the evergreen oak, holly oak or holm oak, is a large evergreen oak native to the Mediterranean region. It takes its name from holm, an ancient name for holly. It is a member of the "Cerris" section of the genus, with acorns that mature in a single summer.


Classification.

The Braconidae are currently divided into about 47 subfamilies and over 1000 genera, which include "Aerophilus", "Aleiodes", "Apanteles", "Asobara", "Bracon", "Cenocoelius", "Chaenusa", "Chorebus", "Cotesia", "Dacnusa", "Diachasma", "Microgaster", "Opius", "Parapanteles", "Phaenocarpa", "Spathius", and "Syntretus."  These fall to two major groups, informally called the cyclostomes and noncyclostomes. In cyclostome braconids, the labrum and the lower part of the clypeus are concave with respect to the upper clypeus and the dorsal margin of the mandibles. These groups may be clades that diverged early in the evolution of braconids.  The former subfamily Trachypetinae, containing three rare Australian genera of large parasitoid wasps, was removed in 2020 to form a new family, Trachypetidae, considered to be sister taxon to the remaining braconids.

Morphology.

The morphological variation among braconids is notable. They are often black-brown (sometimes with reddish markings), though some species exhibit striking coloration and patterns, being parts of Müllerian mimicry complexes. They have one or no recurrent veins, unlike other members of the other family in Ichneumonoidea (Ichneumonidae), which usually have two. Wing venation patterns are also divergent to apparent randomness. The antennae have 16 segments or more; the hind trochanters have two segments.  Females often have long ovipositors, an organ that largely varies interspecifically. This variation is closely related to the host species upon which the wasp deposits its egg. Species that parasitize microlepidopterans, for instance, have longer ovipositors, presumably to reach the caterpillar through layers of plant tissue. Some wasps also have long ovipositors to bypass caterpillar defense mechanisms such as spines or hairs, or to reach deeply-burrowed Coleoptera larvae in tree trunks.

Parasitoidy.

The larvae of most braconids are internal or external primary parasitoids of other insects, especially the larval stages of Coleoptera, Diptera, and Lepidoptera, but also some hemimetabolous insects such as aphids, Heteroptera, or Embiidina. Most species kill their hosts, though some cause the hosts to become sterile and less active. Parasitoidy on adult insects (particularly on Hemiptera and Coleoptera) also occurs. Members of two subfamilies, the Mesostoinae and Doryctinae are known to form galls on plants. Braconids are often used as biological pest control agents, especially against aphids.

Examples of hosts.

Thousands of species of insects are used as hosts by braconid wasps. A few notable examples are detailed here.  Some species of braconids are parasitoids of the Asian corn borer (a lepidopteran moth known for being a pest of maize in East Asia), the African sugarcane borer (a moth commonly found in sub-Saharan Africa), the butterfly "Danaus chrysippus" in Ghana, and the american serpentine leafminer and tomato hornworm in North America. Braconids often will prey on fruit fly larvae like "A. suspensa" as well.

Polydnaviruses.

Endoparasitoid species often display elaborate physiological adaptations to enhance larval survival within the host, such as the co-option of endosymbiotic viruses for compromising host immune defenses. These bracoviruses are often used by the wasps instead of, or in addition to, a venom cocktail. The DNA of the wasp actually contains portions that are the templates for the components of the viral particles and they are assembled in an organ in the female's abdomen known as the calyx. A 2009 study has traced the origins of these templates to a 100-million-year-old viral infection whose alterations to its host DNA provided the necessary basis for these virus-like "templates".  These viruses suppress the immune system and allow the parasitoid to grow inside the host undetected. The exact function and evolutionary history of these viruses are unknown. Sequences of polydnavirus genes show the possibility that venom-like proteins are expressed inside the host caterpillar. Through the evolutionary history of being used by the wasps, these viruses apparently have become so modified, they appear unlike any other known viruses today. Because of this highly modified system of host immunosuppression, a high level of parasitoid-host specificity is not surprising.

Evolutionary history.

The family seems to date from early Cretaceous (provided that "Eobracon" is properly assigned to this family). It underwent extensive diversification from mid or late Cretaceous to early Cenozoic, correlating with the radiation of flowering plants and associated insect herbivores, the main hosts of braconids.

Differentiation from Ichneumonidae.

Braconids are distinguished from their sister group Ichneumonidae by these character combinations. In Braconidae, vein 2m-cu of the forewing is absent except in the Chilean species "Apozyx penyai" - this vein is present in 95% of Ichneumonidae. Vein 1/Rs+M of the forewing is 85% present in Braconidae, but absent in all Ichneumonidae. Vein 1r-m of the hind wing is in 95% of Braconidae basal to the separation of R1 and Rs (it is opposite or apical in Ichneumonidae). In Braconidae, metasomal tergum 2 is fused with tergum 3, (secondarily flexible in Aphidiinae) - 90% of Ichneumonidae have a flexible suture.

Other characteristics.

The species "Microplitis croceipes" possesses an extremely accurate sense of smell and can be trained for use in narcotics and explosives detection.  At least some braconids appear to be very resistant to ionizing radiation. While a dose of 400 to 1000 rads can kill an average human, a dose of 180,000 rads was required to kill a braconid of genus "Habrobracon" in an experiment.

External links.

Species profiles from the University of Florida Institute of Food and Agricultural Sciences:

The Braconidae are a family of parasitoid wasps. After the closely related Ichneumonidae, braconids make up the second-largest family in the order Hymenoptera, with about 17,000 recognized species and many thousands more undescribed. One analysis estimated a total between 30,000 and 50,000, and another provided a narrower estimate between 42,000 and 43,000 species.


Proof sketch.

The proof relies on transforming the differential equation, and applying fixed-point theory. By integrating both sides, any function satisfying the differential equation must also satisfy the integral equation  A simple proof of existence of the solution is obtained by successive approximations. In this context, the method is known as Picard iteration.  Set  and  It can then be shown, by using the Banach fixed point theorem, that the sequence of "Picard iterates" is convergent and that the limit is a solution to the problem. An application of Grönwall's lemma to, where and are two solutions, shows that, thus proving the global uniqueness (the local uniqueness is a consequence of the uniqueness of the Banach fixed point).  Picard's method is most often stated without proof or graphing. See Newton's method of successive approximation for instruction.

Example of Picard iteration.

Let formula_6 the solution to the equation formula_7 with initial condition formula_8 Starting with formula_9 we iterate  so that formula_11:  and so on. Evidently, the functions are computing the Taylor series expansion of our known solution formula_15 Since formula_16 has poles at formula_17 this converges toward a local solution only for formula_18 not on all of R.

Example of non-uniqueness.

To understand uniqueness of solutions, consider the following examples. A differential equation can possess a stationary point. For example, for the equation (formula_19), the stationary solution is, which is obtained for the initial condition. Beginning with another initial condition, the solution "y"("t") tends toward the stationary point, but reaches it only at the limit of infinite time, so the uniqueness of solutions (over all finite times) is guaranteed.  However, for an equation in which the stationary solution is reached after a "finite" time, the uniqueness fails. This happens for example for the equation, which has at least two solutions corresponding to the initial condition such as: or  so the previous state of the system is not uniquely determined by its state after "t" = 0. The uniqueness theorem does not apply because the function has an infinite slope at and therefore is not Lipschitz continuous, violating the hypothesis of the theorem.

Detailed proof.

Let  where:  This is the compact cylinder where is defined. Let  this is, the maximum slope of the function in modulus. Finally, let "L" be the Lipschitz constant of with respect to the second variable.  We will proceed to apply Banach fixed point theorem using the metric on formula_24 induced by the uniform norm  We define an operator between two functional spaces of continuous functions, Picard's operator, as follows:  defined by:  We must show that this operator maps a complete non-empty metric space X into itself and also is a contraction mapping.  We first show that, given certain restrictions on formula_28 takes formula_29 into itself in the space of continuous functions with uniform norm. Here, formula_29 is a closed ball in the space of continuous (and bounded) functions "centered" at the constant function formula_31. Hence we need to show that  implies  where formula_34 is some number in formula_35 where the maximum is achieved. The last step is true if we impose the requirement.  Now let's try to prove that this operator is a contraction.  Given two functions formula_36, in order to apply the Banach fixed point theorem we want  for some "q" < 1. So let "t" be such that  then using the definition of Γ  This is a contraction if formula_40  We have established that the Picard's operator is a contraction on the Banach spaces with the metric induced by the uniform norm. This allows us to apply the Banach fixed point theorem to conclude that the operator has a unique fixed point. In particular, there is a unique function  such that. This function is the unique solution of the initial value problem, valid on the interval "I" where "a" satisfies the condition

Optimization of the solution's interval.

Nevertheless, there is a corollary of the Banach fixed point theorem: if an operator "T" is a contraction for some "n" in N, then "T" has a unique fixed point. Before applying this theorem to the Picard operator, recall the following: Lemma: formula_43 "Proof." Induction on "m". For the base of the induction we have already seen this, so suppose the inequality holds for, then we have:  This inequality assures that for some large "m",  and hence Γ will be a contraction. So by the previous corollary Γ will have a unique fixed point. Finally, we have been able to optimize the interval of the solution by taking  In the end, this result shows the interval of definition of the solution does not depend on the Lipschitz constant of the field, but only on the interval of definition of the field and its maximum absolute value.

Other existence theorems.

The Picard–Lindelöf theorem shows that the solution exists and that it is unique. The Peano existence theorem shows only existence, not uniqueness, but it assumes only that is continuous in, instead of Lipschitz continuous. For example, the right-hand side of the equation with initial condition is continuous but not Lipschitz continuous. Indeed, rather than being unique, this equation has three solutions:  Even more general is Carathéodory's existence theorem, which proves existence (in a more general sense) under weaker conditions on. Although these conditions are only sufficient, there also exist necessary and sufficient conditions for the solution of an initial value problem to be unique, such as Okamura's theorem.

In mathematics – specifically, in differential equations – the Picard–Lindelöf theorem, Picard's existence theorem, Cauchy–Lipschitz theorem, or existence and uniqueness theorem gives a set of conditions under which an initial value problem has a unique solution.


Family.

She was presumably born in Ruthenia, in the domains of her paternal grandfather Michael of Chernigov. Her grandfather was the last Grand Prince of Kiev, who was deposed not by a more powerful prince but by the Mongol Empire. Her parents were Rostislav Mikhailovich, future ruler of Belgrade and Slavonia, and his wife Anna of Hungary. After the death of her father's father, Kunigunda's family relocated to Hungary, where her mother's father, Béla IV of Hungary, made her father governor of certain Serbian-speaking regions in the Danube Valley. Her father proclaimed himself Emperor of Bulgaria in 1256 but did not stay there to defend his title.

Marriage.

Kunigunda was married – as a token of alliance from her maternal grandfather Béla – to King Ottokar II of Bohemia (ca. 1233 – 1278) in Pressburg (now Bratislava) on 25 October 1261. Ottokar was paternally a member of the Přemyslid dynasty whose marriage to Margaret, Duchess of Austria (ca. 1204 – 1266) was annulled.  Kunigunda, 41 years Margaret's junior, bore Ottokar several children including:

Queen and regent of Bohemia.

However, the peace between Bohemia and Hungary ended after 10 years, when Kunigunda's uncle Stephen came to power as the King of Hungary.  In 1278, King Ottokar tried to recover his lands lost to Rudolph I of Germany in 1276. He made allies and collected a large army, but he was defeated by Rudolph and killed at the Battle of Dürnkrut and Jedenspeigen on the March on 26 August 1278.  Moravia was subdued and its government entrusted to Rudolph's representatives, leaving Kunigunda, now Queen Regent of Bohemia in control of only the province surrounding Prague, while the young Wenceslaus was betrothed and married to one of Rudolph's daughters, Judith.  Kunigunda married secondly a Bohemian magnate Záviš, Lord of Falkenštejn, in Prague in 1285. However, she died only a few months later. Záviš survived her and married again to the Hungarian Princess Elisabeth. He was executed on behalf of the King on 24 August 1290.  Kunigunda's son Wenceslaus II kept the Kingdom of Bohemia, and also succeeded in obtaining Poland and Hungary although not very sustainably. Ultimately, she is one of the pivotal ancestresses of both the House of Luxembourg and the Habsburgs.

Kunigunda Rostislavna (1245 – 9 September 1285; Czech: "Kunhuta Uherská" or "Kunhuta Haličská") was Queen consort of Bohemia and its Regent from 1278 until her death. She was a member of the House of Chernigov, and a daughter of Rostislav Mikhailovich.