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Under U.S. tax rules, the de minimis rule governs the treatment of small amounts of market discount. Under the rule, if a bond is purchased with a small amount of market discount (an amount less than 0.25% of the face value of a bond times the number of complete years between the bond's acquisition date and its maturity date) the market discount is considered to be zero and the discount on the ...
Then the negligible sets form an ideal. This idea can be applied to any infinite set; but if applied to a finite set, every subset will be negligible, which is not a very useful notion. Or let X be an uncountable set, and let a subset of X be negligible if it is countable. Then the negligible sets form a sigma-ideal.
In the covering theorem, the aim is to cover, up to a "negligible set", a given set E ⊆ R d by a disjoint subcollection extracted from a Vitali covering for E : a Vitali class or Vitali covering for E is a collection of sets such that, for every x ∈ E and δ > 0, there is a set U in the collection such that x ∈ U and the diameter of U is ...
In complexity-based modern cryptography, a security scheme is provably secure if the probability of security failure (e.g., inverting a one-way function, distinguishing cryptographically strong pseudorandom bits from truly random bits) is negligible in terms of the input = cryptographic key length .
These elements are also maximal and minimal elements, respectively, of the red subset. In mathematics , especially in order theory , the greatest element of a subset S {\displaystyle S} of a partially ordered set (poset) is an element of S {\displaystyle S} that is greater than every other element of S {\displaystyle S} .
Negligible senescence is a term coined by biogerontologist Caleb Finch to denote organisms that do not exhibit evidence of biological aging , such as measurable reductions in their reproductive capability, measurable functional decline, or rising death rates with age. [1]
In 1945 Prigogine [44] (see also Prigogine (1947) [60]) proposed a “Theorem of Minimum Entropy Production” which applies only to the purely diffusive linear regime, with negligible inertial terms, near a stationary thermodynamically non-equilibrium state. Prigogine's proposal is that the rate of entropy production is locally minimum at ...
Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖ 2 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC [2] and non-negative matrix/tensor factorization. [3] [4] The latter can be considered a generalization of ...