• ###### proofs
• Structured derivations (SD) is a logic-based format for presenting mathematical solutions and proofs created by Prof. Ralph-Johan Back and Joakim von Wright at Åbo Akademi University, Turku, Finland. (wikipedia.org)
• ###### displaystyle
• If ( R , δ ) {\displaystyle (R,\delta )} is a ring with a p-derivation, then the map σ ( x ) := x p + p δ ( x ) {\displaystyle \sigma (x):=x^{p}+p\delta (x)} defines a ring endomorphism which is a lift of the frobenius endomorphism. (wikipedia.org)
• If R is any p-torsion free ring and σ : R → R {\displaystyle \sigma :R\to R} is a lift of the Frobenius endomorphism then δ ( x ) = σ ( x ) − x p p {\displaystyle \delta (x)={\frac {\sigma (x)-x^{p}}{p}}} defines a p-derivation. (wikipedia.org)
• Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: D ( a b ) = D ( a ) b + a D ( b ) . {\displaystyle D(ab)=D(a)b+aD(b). (wikipedia.org)
• If A is a K-algebra, for K a ring, and D : A → A {\displaystyle D:A\to A} is a K-derivation, then If A has a unit 1, then D(1)=D(12)=2D(1), so that D(1)=0. (wikipedia.org)
• There is an A-module Ω A / K {\displaystyle \Omega _{A/K}} (called the Kähler differentials) with a K-derivation d : A → Ω A / K {\displaystyle d:A\to \Omega _{A/K}} through which any derivation D : A → M {\displaystyle D:A\to M} factors. (wikipedia.org)
• ###### derive
• A derivation-relevant character argument of an operation is an argument used to derive the collation of the operator's result. (oracle.com)
• State derivation has been understood since the 1970s as an attempt within Marxism and neo-Marxism to explain the emergence and extent of the state and its law within the bourgeois, modern economic system and therewith to derive the relationship between economics and politics from the structure of capitalist production. (wikipedia.org)
• Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys. (wikipedia.org)
• ###### Functions
• citation needed] Modern password-based key derivation functions, such as PBKDF2 (specified in RFC 2898), use a cryptographic hash, such as SHA-2, more salt (e.g. 64 bits and greater) and a high iteration count (often tens or hundreds of thousands). (wikipedia.org)
• ###### occur
• Derivation can also occur without any change of form:telephone (noun) and to telephone. (wikipedia.org)
• It may involve the use of an affix (such as with happy → happiness, employ → employee), or it may occur via conversion (such as with the derivation of the noun run from the verb to run). (wikipedia.org)
• ###### Guidelines
• James, J. and Ramanathan, R., "Spacecraft Water Exposure Guidelines: Derivation by Toxicological Risk Assessment Methods," SAE Technical Paper 2002-01-2536, 2002, https://doi.org/10.4271/2002-01-2536 . (sae.org)
• ###### Definition
• For each guideline discussed, a definition and description of the derivation and applicability or intended use are provided to enable you to determine if a comparison value is appropriate to use for evaluating site-specific conditions. (cdc.gov)
• Definition/Derivation. (cdc.gov)
• ###### example
• Generally speaking, inflection applies in more or less regular patterns to all members of a part of speech (for example, nearly every English verb adds -s for the third person singular present tense), while derivation follows less consistent patterns (for example, the nominalizing suffix -ity can be used with the adjectives modern and dense, but not with open or strong). (wikipedia.org)
• For example, when the affix -er, is added to an adjective, as in small-er, it acts as an inflection, but when added to a verb, as in cook-er, it acts as a derivation. (wikipedia.org)
• ###### Table
• In order to assist Code users in the transition to the new Code's organization, the Derivation Table indicates where chapters and articles of the 1975 Code have been included in the 2011 Code, or the reason for exclusion. (ecode360.com)
• An argument that is a format model, a pattern, a flag string, or a key into a virtual table of system information is not considered a derivation-relevant argument. (oracle.com)
• ###### important
• However, it is important to note that derivations and inflections can share homonyms, that being, morphemes that have the same sound, but not the same meaning. (wikipedia.org)
• The intent of this article is to highlight the important points of the derivation of the Navier-Stokes equations as well as its application and formulation for different families of fluids. (wikipedia.org)
• ###### exact
• The derivation is exact and axonal delays and memory effects such as refractory behavior are taken into account. (springer.com)
• ###### order
• I'm hoping to get a further insight on the derivation of the variation of parameters method used in ordinary differential equations to solve linear second order equations. (physicsforums.com)
• ###### known
• When writing a proof or a solution as a structured derivation, all known information is listed in the beginning as assumptions. (wikipedia.org)
• ###### process
• The process of determining the collation of a character result of an SQL operation is called collation derivation. (oracle.com)
• ###### respect
• In that respect, derivation differs from compounding by which free morphemes are combined (lawsuit, Latin professor). (wikipedia.org)
• ###### original
• Such use may be expressed as DK=KDF(Key, Salt, Iterations) where DK is the derived key, KDF is the key derivation function, Key is the original key or password, Salt is a random number which acts as cryptographic salt, and Iterations refers to the number of iterations of a sub-function. (wikipedia.org)
• ###### approach
• The calculational approach is limited to writing proof fragments, and longer derivations are commonly decomposed into several separate subproofs. (wikipedia.org)
• ###### generally
• In such applications, it is generally recommended that the key derivation function be made deliberately slow so as to frustrate brute-force attack or dictionary attack on the password or passphrase input value. (wikipedia.org)
• More generally, if M is an A-bimodule, a K-linear map D : A → M that satisfies the Leibniz law is also called a derivation. (wikipedia.org)
• more generally it is a derivation on the tensor algebra of a manifold. (wikipedia.org)
• ###### time
• This derivation only uses the star's coordinates at the time of emission, and therefore has the formal advantage there is no place for the relative velocity of the star towards the astronomer and therefore it is evident that the observed position doesn't depend on the star's velocity - provided that the resultant change of position is much smaller than the distance between star and Earth. (wikipedia.org)
• ###### seen
• Within the state-derivation debate the state is seen as a "structural component of the capitalist relations of production itself, its specific political form. (wikipedia.org)