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If the mean =, the first factor is 1, and the Fourier transform is, apart from a constant factor, a normal density on the frequency domain, with mean 0 and variance /. In particular, the standard normal distribution φ {\textstyle \varphi } is an eigenfunction of the Fourier transform.
Task 1: "Answer retrieval" matching old post answers to newly posed questions, and Task 2: "Formula retrieval" matching old post formulae to new questions. Starting with the domain of mathematics, which involves formula language, the goal is to later extend the task to other domains (e.g., STEM disciplines, such as chemistry, biology, etc ...
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
[citation needed] The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1. Boolean algebra is the starting point of mathematical logic and has important applications in electrical engineering and computer science .
The ratio varies from 0 to 1. The surface of a perfect black body (with an emissivity of 1) emits thermal radiation at the rate of approximately 448 watts per square metre (W/m 2) at a room temperature of 25 °C (298 K; 77 °F). Objects have emissivities less than 1.0, and emit radiation at correspondingly lower rates. [1]
Germany, [e] officially the Federal Republic of Germany, [f] is a country in Central Europe.It lies between the Baltic and North Sea to the north and the Alps to the south. Its sixteen constituent states have a total population of over 82 million in an area of 357,596 km 2 (138,069 sq mi), making it the most populous member state of the European Union.
The Congressional Budget Office estimated in March 2009 that under the Obama administration public debt would rise from 40.8% of GDP in 2008 to 70.1% in 2012. [63] Gross debt did rise to 84.5% of GDP at the end of Fiscal Year 2009 and to 93.5% of GDP at the end of the fiscal year 2010.
The history of England during the Late Middle Ages covers from the thirteenth century, the end of the Angevins, and the accession of Henry II – considered by many to mark the start of the Plantagenet dynasty – until the accession to the throne of the Tudor dynasty in 1485, which is often taken as the most convenient marker for the end of the Middle Ages and the start of the English ...