With unitary normalization constants, the DFT becomes a unitary transformation, defined by a unitary matrix:

With this transformation, police command and control became more centralized.

With the prospect of continued relocation of labor-intensive industries to economies with cheaper work forces, such as in China and Vietnam, Taiwan's future development will have to rely on further transformation to a high technology and service-oriented economy.

With the growth of the economy of the country, Yerevan has been undergoing major transformation as many parts of the city have been the recipient of new construction since the early 2000s, and retail outlets such as restaurants, shops and street cafes, which were rare during Soviet times, have multiplied.

With the Respect for History Project, launched in February 2006, a great transformation has taken place within the borders of Gallipoli Peninsula Historical National Park.

With the falling of any significant rains comes a transformation of dormant wildflowers.

With the turn of the century came industrialization, and Western Pennsylvania ’ s role was vital in the transformation of the national economy.

With his transformation into Galvatron, Megatron departed from the Japanese G1 continuity ( which took a different direction after the end of series 3, opting to replace the events of The Rebirth with those of Headmasters ), until five years later, in the manga-exclusive storyline, Battlestars: The Return of Convoy, which, although not animated itself ( told instead through one chapter of manga and color magazine spreads ), continues the tale of the cartoon Universe.

With his usual tireless activity, he supervised the transformation of Lobau island into a huge army base.

With a subsequent grant from the NIMH he studied American politics and reported that " a spiritual crisis " was at the heart of the political transformation of American society as well as at the heart of much of the psychic pain that was being treated in individual therapy.

With motion parallel to the x-axis, the transformation acts on only two components:

Note that natural transformations can be composed: if μ ( X ): F ( X ) → G ( X ) is a natural transformation from the functor F: C → D to the functor G: C → D, and η ( X ): G ( X ) → H ( X ) is a natural transformation from the functor G to the functor H, then the collection η ( X ) μ ( X ): F ( X ) → H ( X ) defines a natural transformation from F to H. With this composition of natural transformations ( known as vertical composition, see natural transformation ), D < sup > C </ sup > satisfies the axioms of a category.

With v as invariant and the transforming covariant, it must be that the ( the set of numbers identifying the components ) transform in a different way, the inverse called the contravariant transformation rule.

With his transformation capabilities restored ( the explanation for which was not offered in the American series ), Grimlock was Optimus Prime's second in command in the so called Generation 2 series, aiding in the Autobots ' war against the " second generation " of Cybertronians led by Jhiaxus.

With the historical changes, like the cultural revolution and the influence of various religions, arts and sports, led to the transformation of various aspects of culture within races and the ethnic group in China.

With an investment of more than US $ 27. 000. 000, Airplan began the transformation in the Olaya Herrera Airport, located in the city of Medellín, under the parameters defined in the concession contract concluded between the company operates, and the Civil Aeronáutuica Public Establecimeinto Olaya Herrera.

With Gospel values we dialogue with peoples of different cultures, faiths, and religions, in the search for an integral transformation of society ; we work with others to safeguard human dignity, nurture family, foster harmony, promote a culture of peace, and respond to the calls of justice and integrity of creation ”

With the exception of Jones, who had witnessed his very first transformation into the Hulk, Banner managed for many years to keep his condition a secret not only from the rest of the world but also from Betty, as this secret also served to alienate her from him.

With BRAC initiatives and transformation, proposed changes will make the Army Reserve more deployable and functional in order to serve America ’ s military needs in the 21st century.

With these conservation laws, Miura showed a connection ( called the Miura transformation ) between solutions of the KdV and MKdV equations.

" With Elizabeth II's ascension occurring during the transformation of the British Empire into the Commonwealth of Nations, the Commonwealth Realms collectively decided to each create a title for the Sovereign within their own jurisdictions, though it would retain the common format of " Elizabeth the Second, by the Grace of God of the United Kingdom, country and Her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith.

With these new additions playing superbly and aided by tremendous seasons of veterans Dick Thornton, Peter Martin, Dick Aldridge, Mel Profit, and Marv Luster among others, the Argos rolled to a record of 10-4 and a first place finish in the East.

With treatment in hand, Hitchcock shopped for a screenwriter ; he wanted a " name " writer to lend some prestige to the screenplay, but was turned down by eight writers, including John Steinbeck and Thornton Wilder, all of whom thought the story too tawdry and were put off by Highsmith's first-timer status.

In Josephine Pullein-Thompson's " Pony Club Team " the second novel in her " West Barsetshire Pony Club " series, Landor's " I Strove With None " is quoted by both Noel Kettering and Henry Thornton

With the NHL set to resume in 2005 – 06, Thornton became a restricted free agent in the summer of 2005 and was reportedly unhappy with the state of the Bruins franchise, as well as the criticism of his play in the Bruins ' early playoff exit in 2004.

With a league-leading 92 assists, Thornton became only the third player in NHL history to record back-to-back 90-assist seasons, joining Wayne Gretzky and Mario Lemieux.

With Mantler, she co-led the Jazz Composers ' Orchestra and started the JCOA record label which issued a number of historic recordings by Clifford Thornton, Don Cherry and Roswell Rudd, as well as her own magnum opus Escalator Over The Hill and Mantler's The Jazz Composer's Orchestra LPs.

With 67 assists, he led the league for a third consecutive season, becoming the fifth player in league history to do so after Joe Thornton ( 2005 – 08 ), Wayne Gretzky ( 1979 – 92 ), Bobby Orr ( 1969 – 72 ) and Stan Mikita ( 1964 – 67 ).

With limited time to prepare, Thornton crams for exams with help from Jason, Derek, Lou and Diane.

With Teri Thornton

With a two-track confluence or blended approach of teaching and coaching, a student at Thornton was afforded the opportunity to transition away or change lanes from a pedagogical practice to progress and sustain an independent andragogical approach to, and a lifetime desire for learning and development.

With the retirement of both Mackey and Greig to private life and scholarly study in Toronto, Thornton Hall closed in 1997.

With the 1676 Quintipartite Deed more accurate surveys and maps were made resulting in the Thornton line, drawn around 1696, and the Lawrence line, drawn around 1743, which was adopted as the final line for legal purposes.

With the rapid rate of closure, the approach from below, the side, and ahead, there would be only a moment when damage could be done.

This arrangement was for Copernicus literally monstrous: `` With ( the Ptolemaists ) it is as though an artist were to gather the hands, feet, head and other members for his images from divers models, each part excellently drawn, but not related to a single body ; ;

With the Discours de la methode and the Principia the things undreamt of in Horatio's philosophy seem to pass from the world.

With the rise to power of the middle class the centre of gravity in human affairs shifted from the public to the private.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

Some memorable plays have been drawn from books, notably Life With Father and Diary Of Anne Frank.

With respect to Article 2,, paragraphs 1 ( B ) and 1 ( C ): Uses of Section 104 ( E ) and Section 104 ( G ) rupees: The Government of India will use the amount of rupees granted or loaned to it by the United States pursuant to paragraphs 1 ( B ) and 1 ( C ) for projects to promote economic development with emphasis upon the agricultural sector including food reserve storage structures and facilities as may from time to time be agreed upon by the authorized representatives of the United States and the authorized representatives of the Government of India, in the following sectors: A.

With respect to skywave service rendered at night, class 1, -- A stations are the only stations permitted to operate in the United States on clear channels specified for class 1, -- A operation, and so render skywave service free from cochannel interference whereever they may be received ; ;

`` With a 15,500-lb. fork-lift, dealers can unload unitized lumber from wide-door box cars for $.30/mbf compared with $1.65 or more to unload loose lumber one piece at a time '', says James Wright of Aj.

With faint heart and a brave smile, I endured his long absences from Chateau Belletch, his coldness, his indifference, his slights and his abuse.

With this seven-word sentence -- though the speaker undoubtedly thought he was dealing only with the subject of food -- he was telling things about himself and, in the last two examples, revealing that he had departed from the customs of his culture.

With the end of the trial Diane disappeared from New York.

With difficulty, Hudson persuaded him to rejoin the ship, and they sailed from Iceland.

With these completed and ice gone from the St. Peter's River ( present-day Minnesota river ) their 250 bushels of wheat, 100 bushels of oats and barley and 30 bushels of peas and some chickens were loaded onto the flat-bottomed boats and rowed up the river to Big Stone Lake, across into Lake Traverse, and down the Red.

With their customary source of supply cut off, the Fort Garry free traders engaged three men to cart goods to them from the Mississippi country.

With great difficulty he made his way from his native Hungary to Geneva to renew his contacts as a member of the Provisional Committee for the World Council of Churches.

With the loss of the Mobile trade, which ended all profits from Louisiana, the Natchez Indians revolted.

With a sturdy act of will she turned her mind away from herself ; ;

With eyes focused on the third congressional district, the historic Delta district, and Congressman Frank E. Smith as the one most likely to go, the redistricting battle will put to a test the longstanding power which lawmakers from the Delta have held in the Legislature.

With cash receipts from marketings expected to be slightly above 1960, farmers' gross income is estimated at $39.5 billion, $1.5 billion above 1960's record high.

With this ultimate weapon, the two Yankees may have saved baseball from its dullest season.

With this act of disobedience, and not with the inception of his individual existence, man began the downward circuit on the spiral of history, descending from the created capacity for immortality to an inescapable mortality.

With such a dream arising, at least in part, from the Protestant heritage of the United States and built into the foundations of the nation, it is not surprising that many efforts were made to give it concrete expression.

With the loss of the study of ancient Greek in the early medieval Latin West, Aristotle was practically unknown there from c. AD 600 to c. 1100 except through the Latin translation of the Organon made by Boethius.