A quantity that grows exponentially (or geometrically) is one whose growth rate is always proportional to its current size. Such growth is said to follow an exponential law. This implies that for any exponentially growing quantity, the larger the quantity gets, the faster it grows. But it also implies that the relationship between the size of the dependent variable and its rate of growth is governed by a strict law, of the simplest kind: direct proportion. It is proved in calculus that this law requires that the quantity is given by the exponential function, if we use the correct time scale. This explains the name.
It may well be the most potent force in the universe.
The cut-and-paste paradigm was widely popularized by Apple in the Lisa (1981) and Macintosh (1984) operating systems and applications. It was mapped to a key combination consisting of a special control key held down while typing the letters X (for cut), C (for copy), and V (for paste).
The Japanese Government has reacted angrily after a North Korean missile flew over its territory. Officials in Tokyo say the medium-range ballistic missile test-fired by North Korea on Monday landed in the Pacific Ocean, travelling much further than previously thought. Japanese Government officials said the missile was composed of two stages, the first of which landed in the Sea of Japan, with the second falling in waters off Japan's north-east coast. If confirmed, the test is the first reported launch by North Korea of a two-stage missile and marks a significant step forward in its rocket technology. 'Strong protest' The Japanese Prime Minister Keizo Obuchi said on Monday his government had been aware of North Korea's preparations to launch a ballistic missile into the waters that divide the Korean peninsula from Japan. As a result, Japan has refused to sign an agreement on sharing the cost of providing safer nuclear reactors to North Korea and will protest to the North Koreans. Chief Cabinet Secretary Hiromu Nonaka expressed Japan's "strong protest" in a complaint to North Korea's representative at the United Nations. Tokyo and Pyongyang have no diplomatic relations. "It was an extremely dangerous act to conduct without any advance notice in the sea near Japan where a number of vessels and aircraft of our country are operating," Mr Nonaka said. US concern The United States expressed concern over the North Korean action. Correspondents say it is likely to overshadow talks which have resumed in New York between Washington and Pyongyang on the progress of an agreement by North Korea in 1994 to freeze its nuclear reprocessing programme. North Korea's test programme Russian officials have said the missile launch was a test which misfired. They announced the missile had landed inside their territorial waters and are reported to have sent warships to the area to investigate. South Korea's Defence Ministry identified the missile as a newly-developed Taepo-Dong One, with an estimated range of approximately 1,000 miles. In 1993, North Korea caused anxiety in Japan by test-firing a medium-range Rodong-1 missile into the Sea of Japan, demonstrating that parts of western Japan were within the 1,000km (600-mile) range of the missile. The BBC Tokyo correspondent says there is speculation that the latest missile firing was intended by North Korea as a show of power in advance of the 50th anniversary of the founding of the Stalinist state.
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