Under a Galilean transformation the equations of Newtonian dynamics are invariant, whereas those of electromagnetism are not.

In the case of transformation laws in quantum mechanics, the requisite automorphisms are unitary ( or antiunitary ) linear transformations of the Hilbert space V. Under Galilean relativity or special relativity, the mathematics of frames of reference is particularly simple, and in fact restricts considerably the set of physically meaningful observables.

Under Lorentz transformations, the time and distance between events may differ among inertial reference frames ; however, the Lorentz scalar distance s between two events is the same in all inertial reference frames

Under simple expansions and contractions of the coordinates, the reciprocity is exact ; under affine transformations the components of a vector intermingle on going between covariant and contravariant expression.

Under the projective transformations, the incidence structure and the relation of projective harmonic conjugates are preserved.

Under the former system, poor countries were encouraged to undergo social and economical structural transformations as part of their development, creating industrialization and intentional industrial policy.

Under gauge transformations, the angular momentum transforms as

Under Poincaré's definition, an automorphic function is one which is analytic in its domain and is invariant under a denumerable infinite group of linear fractional transformations.

Under the direction of John Neschling from 1997 to 2008, the orchestra went through major transformations which positioned them as a reference for quality and excellence in the fields of art, culture, and education in Brazil.

Under linear coordinate transformations on the manifold, it behaves like a tensor, but under general coordinate transformations, it does not.

Under those transformations the equations preserve their form for some types of accelerated motions.

Under unusual circumstances a resident individual may be granted an extension of time to file a return.

Under Clinton, the United States had a projected federal budget surplus for the first time since 1969.

Under extreme climatic conditions, a biennial plant may complete its life cycle in a very short period of time ( e. g. three or four months instead of two years ).

Under Palmer, the team advanced to the playoffs for the first time since 1990 in the 2005 season, which also was the first time the team had a winning percentage above. 500 since 1990.

Under Java or C ++ the visibility of an object is defined in the code itself, meaning that to support a similar change the programmer would be forced to re-write the definitions completely, and could not have two versions at the same time.

He performed a " work in progress " version of Under Milk Wood, solo, for the first time at Harvard University on 3 May.

Under Ron Greenwood they managed to qualify for the 1982 World Cup in Spain ( the first time competitively since 1962 ), but were eliminated from a second qualifying round comprising further group matches without losing a game all tournament.

Under American football's tuck rule, if the quarterback is attempting to bring the ball back to his body after starting a passing motion, a lost ball may be considered an incomplete pass even if the quarterback's arm is moving backward at the time.

Under pressure from his producers, Fellini finally settled on 8½, a self-referential title referring principally ( but not exclusively ) to the number of films he had directed up to that time.

Under the Second Spanish Republic, women were allowed to vote in general elections for the first time.

Under the leadership of coach Osvaldo Bagnoli, in 1982 – 1983 the team secured 4th place in Serie A ( its highest finish at the time ) and even lead the Serie A standings for a few weeks.

Under Icon the find function is a generator, and will return the next instance of the string each time it is resumed before finally failing after it passes the end of the string.

Under some conventions – e. g. the European Convention on Human Rights – individuals or states are permitted, subject to certain conditions, to take individual cases to the enforcement mechanisms ; under most, however ( e. g. the UN conventions ), individual access is contingent on the acceptance of that right by the relevant state party, either by a declaration at the time of ratification or accession, or through ratification of or accession to an optional protocol to the convention.

Under the MPC standard, which represents the modern trend, a defendant is not responsible for criminal conduct " if at the time of such conduct as a result of mental disease or defect he lacks substantial capacity either to appreciate the criminality of his conduct or to conform his conduct to the requirements of the law.

Under this new test only perpetrators suffering from severe mental illnesses at the time of the crime could successfully employ the insanity defense.

Under German Imperial control, and even before then, Japanese traders and fishermen from time to time visited the Marshall Islands, although contact with the islanders was irregular.

Under the terms of the Amended Compact of Free Association, the U. S. will provide US $ 57. 7 million per year to the Marshall Islands ( RMI ) through 2013, and then US $ 62. 7 million through 2023, at which time a trust fund, made up of U. S. and RMI contributions, will begin perpetual annual payouts.

Musashi's father, Munisai, also fought against a master of the Yoshioka school and won 2 out of 3 bouts in front of the shogun at the time, Ashikaga Yoshiaki who granted him the title of " Unrivaled Under The Sun ".

Under UNIX this problem was solved over time as programmers agreed on a number of " well known " locations in the file system to serve various duties.

Under rotational grazing, overgrazed plants do not have enough time to grow to the proper height between grazing events.

Under her influence, he became a Pietist Lutheran, and later recorded that at Marie's deathbed ( from typhoid ) he prayed for the first time since his childhood.

Under his leadership, Knoll created new jobs, gave factory workers annual bonuses, established a scholarship program for the children of employees, created retirement plans for employees who didn ’ t have any, and gave workers stock in the company.

All activities refer to a time t. Under certain circumstances ( see chemical equilibrium ) each activity term such as may be replaced by a concentration term,.

Under the new contract with RCA Victor, he recorded " Civilization ," " You Can ’ t Tell the Depth of the Well ," " Say it with a Slap ," “ Valencia ," and " My Flame Went Out Last Night.

One Nation Under a Groove ( Funkadelic, 1978 ) introduces Funkadelica, a nation wherein the Funk rules and can ’ t be either stopped or labeled.

Under this model, a caplet on a LIBOR expiring at t and paying at T has present value

Under Dr. Paige's leadership, HISD contracted with three private schools that were certified by the Texas Education Agency to teach HISD students so their parents didn ’ t have to bus them to schools across the city.

Under this conception, t ' ai chi was represented by the circle divided into the light and the dark, yang and yin, 15px.

Under a $ 6 million contract from NASA, t / Space has developed a plan and re-usable vehicle to support the International Space Station ( ISS ), after the shuttles retire in 2010.

" Under questioning from committee member Jay Inslee Inhofe dismissed the notion that he was less knowledgeable than climate scientists, saying that he ’ d already given “ five speeches on the science .” His testimony included mention of a book of his which he claimed was forthcoming, saying, " I won ’ t tell you what it ’ s about, but it ’ s titled The Hoax.

Under then current law, known as “ Don't ask, don ’ t tell ,” service members who declare that they are gay would have to be discharged, but McHugh indicated he would not pursue any discharges against soldiers who make those statements in private conversations with him.

“ No Dejes Que ” ( Don ’ t Let It ”), “ Estas Dormida ” ( You ’ re Sleeping ), “ Debajo de Tu Piel ” ( Under Your Skin ), and the soaring “ Nubes ” ( Clouds ) would go on to become Mexican rock staples.

**" The Night Has A Thousand Eyes ", "( Let Me Be ) Your Teddy Bear ", "( Till ) I Kissed You ", " Save The Last Dance For Me ", " Only Sixteen ", " Sealed With A Kiss ", " Lipstick On Your Collar ", " From A Jack To A King ", " My Boy Lollipop ", " Ain ’ t That A Shame ", " Don't Ever Change ", " Let's Dance ", " Under The Boardwalk ", " Itsy Bitsy Teeny Weeny Yellow Polka Dot Bikini ", " Dream Lover ", " She Wears Red Feathers ", " Poetry In Motion ", " Blueberry Hill ", " Shakin ' All Over ", " Lucille "

Under ODIEN's watch, the AVIA brand was reintroduced with a new logo, and development of the EURO 4 compliant models and a new 12 t gvm model, the D120, were commenced.