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Generalizations of the Farkas' lemma are about the solvability theorem for convex inequalities, [4] i.e., infinite system of linear inequalities. Farkas' lemma belongs to a class of statements called "theorems of the alternative": a theorem stating that exactly one of two systems has a solution. [5]
In numerical mathematics, one-step methods and multi-step methods are a large group of calculation methods for solving initial value problems. This problem, in which an ordinary differential equation is given together with an initial condition, plays a central role in all natural and engineering sciences and is also becoming increasingly ...
Prophet inequalities are related to the competitive analysis of online algorithms, but differ in two ways.First, much of competitive analysis assumes worst case inputs, chosen to maximize the ratio between the computed value and the optimal value that could have been achieved with knowledge of the future, whereas for prophet inequalities some knowledge of the input, its distribution, is ...
By the above laws, one can add or subtract the same number to all three terms, or multiply or divide all three terms by same nonzero number and reverse all inequalities if that number is negative. Hence, for example, a < b + e < c is equivalent to a − e < b < c − e .
Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS inequality; BRS-inequality; Burkholder's inequality; Burkholder–Davis–Gundy inequalities; Cantelli's inequality; Chebyshev's inequality; Chernoff's inequality; Chung–Erdős inequality; Concentration inequality; Cramér–Rao inequality; Doob's martingale inequality
The company, a unit of Booking Holdings, said in an emailed statement that it was in the early stages of the review process and no firm decision had been made. As of the end of 2023, Booking ...
So, if known bound is asymmetric, e.g. , to use Azuma's inequality, one need to choose = (| |, | |) which might be a waste of information on the boundedness of . However, this issue can be resolved and one can obtain a tighter probability bound with the following general form of Azuma's inequality.
Go to any sports game—whether it’s a high school game or a pro one—and you’re bound to see athletes on the sidelines drinking Gatorade. It’s likely a staple at your local gym too. It’s ...
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