When the observational errors are uncorrelated and the weight matrix, W, is diagonal, these may be written as

When trying to calibrate the Hubble diagram with accurate supernova standard candles, observational evidence for dark energy was obtained in the late 1990s.

" When most people think of the word “ documentary ,” they think of the observational mode that Leacock, Drew, and Pennebaker all played such a huge role in creating.

When the Crimean War broke out in 1854, Keppel gave Brierly an observational post on his new steam line-of-battle ship, St Jean d ' Acre, in the Baltic Fleet.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

`` When working from one of my sketches I square it up and project its linear form freehand to the watercolor sheet with charcoal.

When an occurrence Af is isolated during text reading, a random memory address Af, the address of a cell in the X-region, is computed from the form of Af.

When this and other units combined to form the present group, it was taken on as a continuing fund-raiser.

When a molten metal is mixed with another substance, there are two mechanisms that can cause an alloy to form, called atom exchange and the interstitial mechanism.

When heated to form a solution and then cooled quickly, these alloys become much softer than normal, during the diffusionless transformation, and then harden as they age.

When looking at variations it needs to be kept in mind that different groups of people do not always sign one way and not the other, rather they prefer and use a particular form of a sign more often.

When the Macdonald government fell due to the Pacific scandal in 1873, the Governor General, Lord Dufferin, called upon Mackenzie, who had been chosen as the leader of the Liberal Party a few months earlier, to form a new government.

When Robert Hooke discovered Hooke's law in 1660, he first published it in anagram form, ceiiinosssttuv, for ut tensio, sic vis ( Latin: as the tension, so the force ).

When she became her godly form " Her hair's ambrosia breathed a holy fragrance.

When the grammatical dual form of Ajax is used in the Iliad, it was once believed that it indicated the lesser Ajax fighting side-by-side with Telamonian Ajax, but now it is generally thought that that usage refers to the Greater Ajax and his brother Teucer.

116 .</ ref > When air condenses it becomes visible, as mist and then rain and other forms of precipitation, and as the condensed air cools Anaximenes supposed that it went on to form earth and ultimately stones.

When the Ming Dynasty Chinese astronomer Xu Guangqi adapted the European southern hemisphere constellations to the Chinese system in The Southern Asterisms, he combined Apus with some of the stars in Octans to form the " Exotic Bird " ( 異雀, Yìquè ).

When word of the dam's failure was telegraphed to Pittsburgh, Frick and other members of the South Fork Fishing and Hunting Club gathered to form the Pittsburgh Relief Committee for assistance to the flood victims as well as determining never to speak publicly about the club or the flood.

When he had finished speaking, a member of the audience stood up and suggested that Bavaria should break away from Prussia and form a separate nation with Austria.

When in form, Nimzowitsch was very dangerous with the black pieces, scoring many fine wins over top players.

When used in such fashion, beacons can be considered a form of optical telegraphy.

When certain ionic compounds containing bromine are mixed with potassium permanganate ( KMnO < sub > 4 </ sub >) and an acidic substance, they will form a pale brown cloud of bromine gas.

When amino acids combine, they form a special bond called a peptide bond through dehydration synthesis, and become a polypeptide, or protein.

: When, after the action had thus occurred, his own men returned to each general, Scipio could adopt no fixed plan of proceeding, except that he should form his measures from the plans and undertakings of the enemy: and Hannibal, uncertain whether he should pursue the march he had commenced into Italy, or fight with the Roman army which had first presented itself, the arrival of ambassadors from the Boii, and of a petty prince called Magalus, diverted from an immediate engagement ; who, declaring that they would be the guides of his journey and the companions of his dangers, gave it as their opinion, that Italy ought to be attacked with the entire force of the war, his strength having been nowhere previously impaired.

When a man distinguished himself by deeds of valour, or any form of meritorious conduct, he was often decorated by a chief by being presented with the feathers of this bird.

When Germany invaded Poland in 1939, Western journalists adopted the term blitzkrieg to describe this form of armoured warfare.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext.

When heavy metals or radionuclides form their own pure colloids, the term " Eigencolloid " is used to designate pure phases, e. g., Tc ( OH )< sub > 4 </ sub >, U ( OH )< sub > 4 </ sub >, Am ( OH )< sub > 3 </ sub >.

When Danican's poorly trained men attacked, on 13 Vendémiaire, 1795 — October 5, 1795, in the calendar used in France, at the time — Napoleon ordered his cannon to fire grapeshot into the mob, an act that became known as the " whiff of grapeshot ".

When era is extended to a calendar system, it is known as a calendar era.

When Julius Caesar established his calendar in 45 BC, he set March 25 as the spring equinox.

When the government official Dan Song proposed the Chinese calendar should be reformed in 123 to adopt certain apocryphal teachings, Zhang opposed the idea.

When dates or times are expressed as years with a decimal fraction from J2000, the years are of exactly 365. 25 days, which is the average length of a year in the Julian calendar.

When inserted into the Roman Catholic calendar of saints in 1738, his feast day was assigned to 24 November.

When a feast on the moveable cycle occurs, the feast on the fixed cycle that was set for that calendar day is transferred, with the propers of the feast often being chanted at Compline on the nearest convenient day.

When feasts occurred, they were either determined by lunar cycles or the Egyptian calendar.

When he devised his table, Julian calendar years were identified by naming the consuls who held office that year — he himself stated that the " present year " was " the consulship of Probus Junior ", which he also stated was 525 years " since the incarnation of our Lord Jesus Christ ".

When Horn is shocked to see the year 1961 showing on the wall calendar, the couple assume that the desert heat has made him mentally unstable.

When Saint Thomas Aquinas's feast was inserted into the Roman calendar, for celebration on the same day, the two African saints were thenceforth only commemorated.

When depicted in Aztec codices Tamoanchan is frequently associated with the trecena 1 Calli in the Aztec calendar.

When the 1969 reform of the Catholic calendar moved him to 28 January, they were moved back to 7 March ( see General Roman Calendar ).

When that calendar was revised in 1969, the individual celebrations of St Barbara, St Catherine of Alexandria, St Christopher, and St Margaret of Antioch were dropped, but in 2004 Pope John Paul II reinstated the 25 November optional memorial of Catherine of Alexandria, whose voice was heard by Saint Joan of Arc.

When the Gregorian calendar reform was instituted in 1582, the lunar cycle previously used with the Julian calendar to complete the calculation of Easter dates was adjusted also, in accordance with a ( modification of a ) scheme devised by Aloysius Lilius.

When noting dates occurring within the period, " Old Style " and " New Style " are used to distinguish which calendar was used by the person who recorded the date.

When Annie Clarke's husband John dies from leukaemia at an early age, her close friend Chris Harper, anxious to purchase a comfortable sofa for the visitors lounge in the hospital where he was treated, hits upon the idea of printing a calendar featuring some of the members of the Knapely chapter of the Women's Institute discreetly posing nude while engaged in everyday activities, such as baking and knitting, in order to raise funds.

When the German Grand Prix was part of the Formula One calendar, a German driver did not win until 1995 ; Michael Schumacher won that year and has won 4 times in total ; and his brother Ralf won in 2001.

When Sun Yat-sen declared the foundation of the Republic of China on 2 January 1912, he decreed that this was the 12th day of the 11th month of year 4609 ( epoch: 2698 BC ), but that the state would now be using the solar calendar and count 1912 as the first year of the Republic.

When the calendar system of Anno Domini was first introduced by Dionysius Exiguus in AD 525, he assigned the beginning of the new year to March 25 since, according to Catholic theology, the era of grace began with the Incarnation of Christ.

When the lunar calendar was changed to the Gregorian calendar at the beginning of the Meiji era, the localities in Japan reacted differently and this resulted in three different times of Obon.