Stated otherwise, a function is invertible if and only if its inverse relation is a function on the range Y, in which case the inverse relation is the inverse function.

Stated in more general terms: " it must be very fast, with sporting handling to match ", " it should be sleek and eye-catching " and its price should be " one in a rarefied atmosphere of its own ".

Stated more precisely, an object has infinite helical symmetries if for any small rotation of the object around its central axis there exists a point nearby ( the translation distance ) on that axis at which the object will appear exactly as it did before.

He Stated " The Province of art is to explore the inner mechanisms and extra dimensional areas of life and, out of the exploration, to produce its findings translated into the form of the artist's media.

Stated in mathematical terms, for the Cassie – Baxter state to exist, the following inequality must be true.

Stated in modern terms, they are as follows:

" " Stated most simply, the central hypothesis explored in cultivation research is that those who spend more time watching television are more likely to perceive the real world in ways that reflect the most common and recurrent messages of the television world, compared with people who watch less television, but are otherwise comparable in terms of important demographic characteristics.

Stated in terms of topology alone, a topological space X has a fork if X has a closed subset T with connected interior, whose boundary consists of three distinct elements and for which the boundary of the complement of T's interior ( relative to X ) consists of these same three elements.

").</ ref > Stated in negative terms, the Preamble has been interpreted as meaning that the Constitution was not the act of sovereign and independent states.

Stated reasons for rejecting a patch are because they are coded poorly, or that the feature is frivolous, abusable or overly specialized, and does not belong in the main client.

Stated life expectancy is 10 to 12 years.

Stated another way, the instance is a particular input to the problem, and the solution is the output corresponding to the given input.

Stated differently, a ring is a division ring if and only if the group of units is the set of all non-zero elements.

A Stated Clerk is elected to a four year term and is responsible for the Office of the General Assembly which conducts the ecclesiastical work of the church.

The current Stated Clerk of the General Assembly is the Rev.

Stated differently, the tidal force is a differential force.

Stated simply, the Novikov consistency principle asserts that if an event exists that would give rise to a paradox, or to any " change " to the past whatsoever, then the probability of that event is zero.

Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire.

Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision.

Stated this way, compass and straightedge constructions appear to be a parlour game, rather than a serious practical problem ; but the purpose of the restriction is to ensure that constructions can be proven to be exactly correct, and is thus important to both drafting ( design by both CAD software and traditional drafting with pencil, paper, straight-edge and compass ) and the science of weights and measures, in which exact synthesis from reference bodies or materials is extremely important.

: sentence A is < u > X </ u > entails sentence A is not < u > Y </ u > Stated differently, if the proposition expressed by the sentence A is < u > X </ u > is TRUE, then the proposition expressed by the sentence A is not < u > Y </ u > is also TRUE .</ ref >

" Stated in more modern language, " The equation a < sup > n </ sup > + b < sup > n </ sup > = c < sup > n </ sup > has no solutions for any n higher than two.

Stated equivalently for matrices, the first part reduces a matrix to row echelon form using elementary row operations while the second reduces it to reduced row echelon form, or row canonical form.

Some felt that the adoption of this report provided for a clear local option mentioned, while the Stated Clerk of the General Assembly, Clifton Kirkpatrick went on record as saying, " Our standards have not changed.

The Oxford English Dictionary dates the first written use of the term for a political movement to 1644, but the source cited there, Marchamont Needham's pamphlet The Case for the Commonwealth of England Stated, dates from 1650.

* Stated in the acknowlegments as the inspiration for the setting of Neil Gaiman's The Graveyard Book.

In each academic year, the Senate holds not less than four Stated Meetings for the Conferring of Degrees ; of these Meetings, which, according to ancient usage, are known in the University as " Public Commencements ", two shall be held in Michaelmas Term, and two in Trinity Term.

The Senate also holds a Stated Meeting in Hilary Term for the purpose of transacting business of the Senate other than the conferring of degrees.

Stated another way, the inverse function gives the solution for y of the equation

Stated requirement was for up to 40 aircraft.

Stated below is the list of subjects offered for the A-level examination ( in 2013 ) for private candidates.

Prosser has previously served as Stated Clerk of the General Assembly of the Cumberland Presbyterian Church for 11 years and served 15 years as pastor of the First Cumberland Presbyterian Church in McKenzie, Tennessee until the year 1986.

Stated by actress Tracy Lynn Cruz at the Power Morphicon, her character Ashley and Andros shared a kiss onscreen, but this scene was later edited out for unknown reasons.

* Sen. Joe Biden-Delaware ; Stated he was not interested in the position, and suggested John McCain for the VP spot

Stated as being the first Protoceratops nest discovered to date, the discovery suggests that Protoceratops parents might have cared for their young at nests during at least the early stages of childhood.

Stated reasoning for this referendum was to counter issues such as the claimed ineffectiveness of the CFS and interference in other university ’ s unions.

Stated purpose for uniforms, often set forth in school uniform policies, include reducing clothing expenditures for parents as well as avoiding distinctions among children based on whose parents can afford to buy them fashionable clothing to wear to school.

* STC, Shipping term for cargo quantity description ( Said To Contain ) or ( Stated To Contain ).

Meetings are moderated by an elected synod Moderator with support of the synod's Stated Clerk.

Joseph R. Wilson served as the first permanent clerk of the southern church's General Assembly, was Stated Clerk from 1865 – 1898 and was Moderator of the PCUS General Assembly in 1879.

Stated simply, the security of a cryptosystem should depend solely on the secrecy of the key and the private randomizer.

His lectures to an audience at Oxford University on the topic of the accuracy of the Bible in 1859 were published as the apologetic work The Historical Evidences of the Truth of the Scripture Records Stated Anew in later years.

Historical Evidences of the Scripture Records Stated Anew: With Special Reference to the Doubts and Discoveries of Modern Times.