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Thus the form a x dx + a y dy + a z dz corresponds to the "dual form" a z dx ∧ dy + a y dz ∧ dx + a x dy ∧ dz. Thus, identifying 0-forms and 3-forms with scalar fields, and 1-forms and 2-forms with vector fields: grad takes a scalar field (0-form) to a vector field (1-form); curl takes a vector field (1-form) to a pseudovector field (2-form);
In the quantum mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, ^ = (^ † ^), where is the amount of displacement in optical phase space, is the complex conjugate of that displacement, and ^ and ^ † are the lowering and raising operators, respectively.
William Ray Norwood Jr. (born January 17, 1981), [1] known professionally as Ray J, is an American R&B singer, songwriter, television presenter, and actor. Born in McComb, Mississippi and raised in Carson, California, he is the younger brother of singer and actress Brandy.
James Bond is a fictional character created by British novelist Ian Fleming in 1953. A British secret agent working for MI6 under the codename 007, Bond has been portrayed on film in twenty-seven productions by actors Sean Connery, David Niven, George Lazenby, Roger Moore, Timothy Dalton, Pierce Brosnan and Daniel Craig.
From left to right: the service dress blue rating badge for a special warfare operator first class and a boatswain's mate second class. United States Navy ratings are general enlisted occupations used by the U.S. Navy since the 18th century, which denote the specific skills and abilities of the sailor.
The episodes of the Bleach anime television series are based on Tite Kubo's original manga series of the same name.It is directed by Noriyuki Abe, produced by TV Tokyo, Dentsu and Pierrot, and was broadcast in Japan from October 5, 2004, to March 27, 2012. [1]
Statistical subregions as defined by the United Nations Statistics Division [1]. This is a list of countries and other inhabited territories of the world by total population, based on estimates published by the United Nations in the 2024 revision of World Population Prospects.
In which case the term / is sufficient to describe the rate of change of temperature. If the sun is not warming the water (i.e. / =), but the path x(t) is not a standstill, the time derivative of φ may change due to the path. For example, imagine the swimmer is in a motionless pool of water, indoors and unaffected by the sun.