Since RGB and CMYK spaces are both device-dependent spaces, there is no simple or general conversion formula that converts between them. Conversions are generally done through color management systems, using color profiles that describe the spaces being converted. Nevertheless, the conversions cannot be exact, particularly where these spaces have different gamuts.
The problem of computing a colorimetric estimate of the color that results from printing various combinations of ink has been addressed by many scientists. A general method that has emerged for the case of halftone printing is to treat each tiny overlap of color dots as one of 8 (combinations of CMY) or of 16 (combinations of CMYK) colors, which in this context are known as Neugebauer primaries. The resultant color would be an area-weighted colorimetric combination of these primary colors, except that the YuleNielsen effect ("dot gain") of scattered light between and within the areas complicates the physics and the analysis; empirical formulas for such analysis have been developed, in terms of detailed dye combination absorption spectra and empirical parameters.
An uncompromising foe of heresy, Leo found that in the almanac of Aquileia, Pelagians were received into church communion without formal repudiation of their errors; he wrote to rebuke them, making accusations of culpable negligence, and required a solemn abjuration before a synod.
Manichaeans fleeing the Vandals had come to Rome in 439 and secretly organized there; Leo learned of it around 443, and proceeded against them by holding a public debate with their representatives, burning their books and warning the Roman Christians against them.
His attitude was as decided against the Priscillianists. Bishop Turibius of Astorga, astonished at the spread of the sect in Spain, had addressed the other Spanish bishops on the subject, sending a copy of his letter to Leo, who took the opportunity to exercise Roman policy in Spain. He wrote an extended treatise (21 July 447) against the sect, examining its false teaching in detail and calling for a Spanish general council to investigate whether it had any adherents in the episcopate, but that was prevented by the political circumstances of Spain.
The pre-Capetian House of Bourbon was a noble family, dating at least from the beginning of the 13th century, when the estate of Bourbon was ruled by the Sire de Bourbon who was a vassal of the King of France. The term House of Bourbon ("Maison de Bourbon") is sometimes used to refer to this first house and the House of Bourbon-Dampierre, the second family to rule the seigneury.
In 1272, Robert, Count of Clermont, sixth and youngest son of King Louis IX of France, married Beatrix of Bourbon, heiress to the lordship of Bourbon and member of the House of Bourbon-Dampierre. Their son Louis was made Duke of Bourbon in 1327. His descendant, the Constable of France Charles de Bourbon, was the last of the senior Bourbon line when he died in 1527. Because he chose to fight under the banner of Holy Roman Emperor Charles V and lived in exile from France, his title was discontinued after his death.
The remaining line of Bourbons henceforth descended from James I, Count of La Marche, the younger son of Louis I, Duke of Bourbon. With the death of his grandson James II, Count of La Marche in 1438, the senior line of the Count of La Marche became extinct. All future Bourbons would descend from James II's younger brother, Louis, who became the Count of Vendme through his mother's inheritance. While the most senior branch of the family, the House of Valois, continued to occupy the throne of France, at the death of Charles IV, Duke of Alenon in 1525, all of the princes of the blood royal were Bourbons.
In 1514, Charles, Count of Vendme had his title raised to Duke of Vendme. His son Antoine became King of Navarre, on the northern side of the Pyrenees, by marriage in 1555. Two of Antoine's younger brothers were Cardinal Archbishop Charles de Bourbon and the French and Huguenot general Louis de Bourbon, 1st Prince of Cond. Louis' male-line, the Princes de Cond, survived until 1830. Finally, in 1589, the House of Valois died out and Antoine's son Henry III of Navarre became Henry IV of France.