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

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 the transformation of Thornton from boys ' houses to girls ' houses in 2007, there are now an equal number of girls and boys at the school for the first time in its history.

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 minimal police training, their main role was to increase the strength of police posts, where they functioned as sentries, guards, escorts for government agents, reinforcement to the regular police, and crowd control, and mounted a determined counter-insurgency campaign.

With the dissolution of regular police and military forces, both left and right began forming armed groups in the spring of 1917.

With Frick's support, Himmler ( pushed on by his right hand man, Reinhard Heydrich ) took over the political police of state after state.

This form of transnational policing plays an increasingly important role in United Nations peacekeeping and this looks set to grow in the years ahead, especially as the international community seeks to develop the rule of law and reform security institutions in States recovering from conflict ( Goldsmith and Sheptycki, 2007 ) With transnational police development-aid the imbalances of power between donors and recipients are stark and there are questions about the applicability and transportability of policing models between jurisdictions ( Hills, 2009 ).

With the collapse of the German Empire in 1918, the Pickelhaube ceased to be part of the military uniform, and even the police adopted shakos of a Jäger style.

With Hitler striving for absolute power in Germany, Himmler and Heydrich wished to control the political police forces of all 17 German states.

" With larger numbers, police detained anyone they could and put them in patrol wagons to go to jail, though Inspector Pine recalled, " Fights erupted with the transvestites, who wouldn't go into the patrol wagon ".

With probable cause, police officers may search any area in the vehicle.

With a growing suspicion of his ministers and subjects, Hongwu established the Jinyi Wei, a network of secret police drawn from his own palace guard.

With the decreasing importance of the Adriatic corridor as a smuggling canal ( thanks to the normalization of the Balkans area ) and a series of successful police and judicial operations against it in recent years the Sacra Corona Unita has been reduced to a fraction of its former power, which peaked around the mid-1990s.

With the publication of his sordid autobiographical novel La Confession de Claude ( 1865 ) attracting police attention, Hachette fired him.

With the growing public and political pressure in recent years, since passage of Japan's blanket anti-gambling law, the police are more active in regulating parlors.

With an estimated 5, 000 fans trying to enter through the turnstiles and increasing safety concerns, the police, to avoid fatalities outside the ground, opened a large exit gate ( Gate C ) that ordinarily permitted the free flow of supporters departing the stadium.

With the end of the Cold War, the Austrian military have increasingly assisted the border police in controlling the influx of illegal immigrants through Austrian borders.

With Blanche sightless and in police custody, Hamer tricks her into revealing C. W.

With nothing to occupy her time and an active imagination, she is a frequent visitor to the local police station, where she reports fanciful suspicions regarding neighborhood activities.

With advice from the police, Harry has Annie drive the bus off the busy freeway, through city streets, and eventually onto an incomplete freeway devoid of traffic.

With Cadena on board, Black Flag began national touring in earnest, and arguably saw two peaks: first as a commercial draw ( they sold out the 3, 500-seat Santa Monica Civic Auditorium, a feat they were never able to manage again ); and second, perhaps seeing the peak of attention from police in the Los Angeles area, due to the violence associated with Black Flag and punk rock in general.

With the Vieques conflict, more and more Puerto Ricans began flying Vieques Air Link every day to go to military camps to protest, and the police also had to fly their personnel and the people arrested in those areas on VAL planes at various times.

With the arrival of more and more people came the need for schools, a library, police and fire service, a church, funeral home, a cemetery and a city hall.

With writer James E. Moser, Webb prepared an audition recording, then sought the LAPD's endorsement ; he wanted to use cases from official files in order to demonstrate the steps taken by police officers during investigations.

With a search warrant, police detectives can also search through credit card records and bank statements, hotel registration information, credit reports, answer machine messages, phone conversations, and technology used for communication.