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An inequality is said to be sharp if it cannot be relaxed and still be valid in general. Formally, a universally quantified inequality φ is called sharp if, for every valid universally quantified inequality ψ, if ψ ⇒ φ holds, then ψ ⇔ φ also holds. For instance, the inequality ∀a ∈ R. a 2 ≥ 0 is sharp, whereas the inequality ∀ ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
where denotes the vector (x 1, x 2). In this example, the first line defines the function to be minimized (called the objective function, loss function, or cost function). The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
December 2, 2024 at 10:11 AM. Lachunda Johnson. An angry, drunken grandma has been busted in Tennessee for allegedly stabbing her daughter and grandson with a kitchen knife during a Thanksgiving ...
A former Tennessee teacher who got pregnant after raping a 12-year-old boy pleaded guilty and has been sentenced to 25 years in prison with no parole. On Dec. 20, Alissa McCommon, 39, of Covington ...