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Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
[1] It is named after the Russian mathematician Andrey Markov , although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in analysis , refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second ...
Expanding the overtime to 10 minutes, rather than five, in the 4 Nations Face-Off round robin led to an exciting finish in the Canada-Sweden game - and more important, no shootout. If the league ...
• More than $1 trillion in revenue for federal, state, and local governments; • Lower energy prices for job creators and middle-class families; and • National security strengthened by freedom from dependence on foreign energy supplies. A successful national energy strategy will have a fundamental influence on the well-being of the nation.
A satirical petition ostensibly aiming to crowdfund a trillion dollars to allow Denmark to buy California has received more than 200,000 signatures.
New York Gov. Kathy Hochul met Tuesday with New York City leaders to discuss the "path forward" after four top aides to embattled Mayor Eric Adams resigned amid increasing pressure on Hochul to ...
The less-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the left, <, has been found in documents dated as far back as the 1560s.