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The non-smooth function (top) y = −x 3 H(−x), where H is the Heaviside step function, and (bottom) the 5th partial sum of its Chebyshev expansion. The 7th sum is indistinguishable from the original function at the resolution of the graph.
Link 1 (horizontal distance between ground joints): 2a Chebyshev's plantigrade machine. A Chebyshev Translating Table Linkage, which combines together two cognate linkages: the Chebyshev Linkage and Chebyshev Lambda Linkage.
In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away.
The Vitali covering lemma is vital to the proof of this theorem; its role lies in proving the estimate for the Hardy–Littlewood maximal function.. The theorem also holds if balls are replaced, in the definition of the derivative, by families of sets with diameter tending to zero satisfying the Lebesgue's regularity condition, defined above as family of sets with bounded eccentricity.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 February 2025. There is 1 pending revision awaiting review. General-purpose programming language "C programming language" redirects here. For the book, see The C Programming Language. Not to be confused with C++ or C#. C Logotype used on the cover of the first edition of The C Programming Language ...
Anatoly Alexeyevich Karatsuba (his first name often spelled Anatolii) (Russian: Анато́лий Алексе́евич Карацу́ба; Grozny, Soviet Union, 31 January 1937 – Moscow, Russia, 28 September 2008 [1]) was a Russian mathematician working in the field of analytic number theory, p-adic numbers and Dirichlet series.
The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh(x/a) is the catenary, the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.