Curmudgeon 发表于 2025-3-25 06:53:03
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Set Theory. Relations. Functions,Let . be a relation from . to . and . a relation from . to .. Then we define the . . ○ . of . and . as the set of all (., .) in . × . such that there is an element . in . with . and .. . ○ . is a relation from . to ..maintenance 发表于 2025-3-25 12:15:31
Equations. Functions of one variable. Complex numbers,Let . be the number of changes of sign in the sequence of coefficients ., ., … , ., . in (2.8). The number of positive real roots of .(.) = 0, counting the multiplicities of the roots, is . or . minus a positive even number. If . = 1, the equation has exactly one positive real root.Permanent 发表于 2025-3-25 17:34:10
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Inequalities,If . is convex on the interval . and . is a random variable with finite expectation, then .(.[.]) ≤ .[.(.)] If . is strictly convex, the inequality is strict unless . is a constant with probability 1.NAUT 发表于 2025-3-26 13:54:01
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