By composing this with the Yoneda embedding Y: C → Set < sup > C < sup > op </ sup ></ sup > one obtains a faithful functor C → Set.

By voluntarily embedding fragments of the Terrigen Crystals into his own body, the character could empower former mutants with extreme versions of their superhuman abilities.

By taking the dual category of which we call we get an exact and fully faithful embedding from our category to an abelian category which has enough projective objects and a cogenerator.

By we get an exact and fully faithful embedding from to the category of R-modules.

By the Whitney embedding theorem any second-countable smooth n-manifold can be smoothly embedded in R < sup > 2n </ sup >.

By considering only the points of the tori that are not removed at some stage, an embedding results of the sphere with a Cantor set removed.

By embedding cursor-control characters within the page data, it was also possible to encode simple animations by re-writing parts of the screen already displayed.

By the end of the Episode the Overmind succeeded in embedding itself in the planet's crust.

By Darboux's theorem, the constant rank embedding is locally determined by.

* DOM parsing: By embedding a full-fledged web browser, such as the Internet Explorer or the Mozilla browser control, programs can retrieve the dynamic contents generated by client side scripts.

By the time the child first attacks the actual problem of reading, he is completely familiar and at ease with all of the elements of words.

By late 1166, and the birth of her final child, however, Henry's notorious affair with Rosamund Clifford had become known, and her marriage to Henry appears to have become terminally strained.

By contrast, for Halliday what the child develops is a " meaning potential ".

By late 2374, Worf and Jadzia are married less than a year when they decided to try to have a child despite the extreme difficulties posed by the disparate biologies of Trill and Klingons.

By producing a " child " solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its " parents ".

By his wife, Richenza of Northeim, Lothair had only one surviving child, a daughter Gertrude, born April 18, 1115.

By the end of his term, however, Schmidt had turned away from deficit spending, due to a deteriorating economic situation, and a number of welfare cuts were carried out, including smaller increases in child benefits and higher unemployment and health contributions.

By Berle's account, he continued to play child roles in other films: Bunny's Little Brother, Tess of the Storm Country, Birthright, Love's Penalty, Divorce Coupons and Ruth of the Range.

By Margaret, Edward had two sons, both of whom lived into adulthood, and a daughter who died as a child.

By 1806, rumours that Caroline had taken lovers and had an illegitimate child led to an investigation into her private life.

By the end of the following year, Alexandra's father had ascended the throne of Denmark, her brother George had become King of the Hellenes, her sister Dagmar was engaged to the Tsarevitch of Russia, and Alexandra had given birth to her first child.

By May of the following year, Caroline was pregnant, and her first child Prince Frederick was born on 20 January 1707.

** At the beginning of Ice Cube's music video for the song, " Gangsta Rap Made Me Do It ", from his 2007 album Raw Footage, a line of text states that " By the year 2020, no child will be left behind " which is followed by an Orwellian classroom setting designed as a segue into the song's sarcastic theme of blame-shifting and anti-gansta rap propaganda during the waning days of the presidency of George W. Bush.

By family accounts, she had been an unruly child and had a difficult time learning to read.

In June 1778 " By the ill conduct of his wife found it necessary to send her into Wales in order to work a reformation on her ", the cause of this appears to have been that Jane Nash " Had imposed two spurious children on him as his and her own, notwithstanding she had then never had any child " and she had contracted several debts unknown to her husband, including one for milliners ' bills of £ 300.

By taking a closer look at the nine traits that Thomas and Chess revealed from their study, parents can gain a better understanding of their child ’ s temperament and their own.

By parents having access to this knowledge now helps them to guide their child in ways that respect the child ’ s individual differences.

By the time a child enters kindergarten, he or she is usually able to join in and enjoy group experiences.

By the age of five, nearly every child in the world has been infected with rotavirus at least once.

By encouraging belief in a fictional character, parents allow themselves to be comforted that their child still believes in fantasy and is not yet " grown up ".

By the age of six, Ali had begun her acting career, as a regular child performer on Sesame Street starting in 1985, even appearing with Herbie Hancock in a musical number.

By late 1991, their friendship had developed into a romance that began shortly after Houston ended her alleged affair with comic Eddie Murphy and after Brown's affair with Ward, who later discovered she was pregnant with Bobby's second child following their breakup, ended.

By his first wife Agnes I, Countess of Nevers he had one child, Matilda I, Countess of Nevers.

By contrast, Kabbalism assumed an " eternal Torah " which was not identical to the Torah written in Hebrew.

By the time the Gospels of Luke and Matthew were written, Jesus is portrayed as being the Son of God from the time of birth, and finally the Gospel of John portrays him as the pre-existent Word () as existing " in the beginning ".

Morton wrote the column until 1975 ; it was revived in January 1996 and continues today, written by William Hartston, though the name " By the Way " has been dropped in favour of simply " Beachcomber ".

By convention, the top strand is written from the 5 ' end to the 3 ' end ; thus, the bottom strand is written 3 ' to 5 '.

By the time Esther was written, the foreign power visible on the horizon as a future threat to Judah was the Macedonians of Alexander the Great, who defeated the Persian empire about 150 years after the time of the story of Esther ; the Septuagint version noticeably calls Haman a " bully " ( βουγαῖον ) where the Hebrew text describes him as an Agagite.

By the 1920s, composers of Tin Pan Alley and Broadway used ballad to signify a slow, sentimental tune or love song, often written in a fairly standardized form ( see below ).

By the third century criticism of Christianity had mounted, partly as a defense against it, and the 15 volume Adversus Christianos by Porphyry was written as a comprehensive attack on Christianity, in part building on the pre-Christian concepts of Plotinus.

By 14 he had already written a short adventure novel called The Black Diamonds which was lost for years until published in 2002.

By the time of Howard's suicide in 1936, he had written 21 complete stories, 17 of which had been published, as well as a number of unfinished fragments.

By twice applying the transformation above from the stationary to the rotating frame, the absolute acceleration of the particle can be written as:

By late 1586 she had been persuaded to sanction her trial and execution on the evidence of letters written during the Babington Plot.

By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers.

By the end of the Hittite Empire, the Hittite language had become a written language of administration and diplomatic correspondence.

By the time of the Crusades ( 1096 – 1270 ), horseshoes were widespread and frequently mentioned in various written sources.

By the time of any written language, Tocharian was geographically remote from the other two.

Following his marriage Albéniz settled in Madrid and produced a quantity of music in a relatively short period. By 1886 he had written over 50 piano pieces.

By contrast, homoerotic themes were present in poetry and other literature written by some Muslims from the medieval period onwards and which celebrated love between men.

By the swing era, big bands were coming to rely more on arranged music: arrangements were either written or learned by ear and memorized — many early jazz performers could not read music.

By now numerous books and articles had been written about the Polgár sisters making them famous even outside of the world of chess.

In March 2011, Spader was named to star in By Virtue Fall, a film written and to be directed by Sheldon Turner.

By decree of Ptolemy III Euergetes, all visitors to the city were required to surrender all books and scrolls, as well as any form of written media in any language in their possession which, according to Galen, were listed under the heading " books of the ships ".

By some accounts, the seeds for Luthor's character first appeared in The Reign of the Super-Man, also written by Siegel and Shuster.

By the time the historical written record begins to cover this area, it has already seen a number of invasions sweep over it, leaving social and political upheaval in their wake.