When g ( x ) equals g ( a ), then the difference quotient for is zero because f ( g ( x )) equals f ( g ( a )), and the above product is zero because it equals f ′( g ( a )) times zero.

Laches (; f. French, lâchesse, lâches ) is an " unreasonable delay pursuing a right or claim ... in a way that prejudices the party " When asserted in litigation, it is an equitable defense, or doctrine.

Let ( S, f ) be a game with n players, where S < sub > i </ sub > is the strategy set for player i, S = S < sub > 1 </ sub > × S < sub > 2 </ sub > ... × S < sub > n </ sub > is the set of strategy profiles and f =( f < sub > 1 </ sub >( x ), ..., f < sub > n </ sub >( x )) is the payoff function for x S. Let x < sub > i </ sub > be a strategy profile of player i and x < sub >- i </ sub > be a strategy profile of all players except for player i. When each player i < nowiki >

When f is a strictly monotonic function, then f is injective on its domain, and if T is the range of f, then there is an inverse function on T for f.

When x and y are real variables, the derivative of f at x is the slope of the tangent line to the graph of f at x.

When specializing to the preadditive categories of abelian groups or modules over a ring, this notion of kernel coincides with the ordinary notion of a kernel of a homomorphism, if one identifies the ordinary kernel K of f: A → B with its embedding K → A.

When f is a first-order function ( a function on " simple " values such as integers ), a fixed point is a first-order value.

When informed that no lens currently had a wide enough aperture to shoot a costume drama set in grand palaces using only candlelight, Kubrick bought and retrofitted a special lens for these purposes: a modified Mitchell BNC camera and a Zeiss lens manufactured for the rigors of space photography, with a maximum aperture of f /. 7.

When captured by the Germans, the French guns were designated 7. 5cm GebK 237 ( f ); the Yugoslav guns were designated 7. 5cm GebK 283 ( j ); and Polish guns were possibly designated as 7. 5cm GebK M. 19 ( p ).

When we say that any two models of the above axioms are isomorphic, we mean that for any two models ( R, 0 < sub > R </ sub >, 1 < sub > R </ sub >, +< sub > R </ sub >, *< sub > R </ sub >, ≤< sub > R </ sub >) and ( S, 0 < sub > S </ sub >, 1 < sub > S </ sub >, +< sub > S </ sub >, *< sub > S </ sub >, ≤< sub > S </ sub >), there is a bijection f: R → S preserving both the field operations and the order.

When the functions f < sub > i </ sub > are solutions of a linear differential equation, the Wronskian can be found explicitly using Abel's identity, even if the functions f < sub > i </ sub > are not known explicitly.

When using this notation, f is then intended as an entire equivalence class of maps, using the same letter f for any representative map.

When the functions match, the value of ( f * g ) is maximized.

When a match is found, keep k < sub > f < sub > 1 </ sub ></ sub >, k < sub > b < sub > 1 </ sub ></ sub > as candidate key-pair in a table T. Test pairs in T on a new pair of ( P, C ) to confirm validity.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

When Gianfranco Fini visited Israel in late November 2003 in the function of Italian Deputy Prime Minister, he labeled the racial laws issued by the fascist regime in 1938 as " infamous ", as also Giorgio Almirante, historic leader of MSI, had done before.

When not celebrating Mass but still serving a liturgical function, such as the semiannual Urbi et Orbi papal blessing, some Papal Masses and some events at Ecumenical Councils, cardinal deacons can be recognized by the dalmatics they would don with the simple white mitre ( so called mitra simplex ).

When the domain of the input function is time ( t ), and the domain of the output function is ordinary frequency, the transform of function s ( t ) at frequency ƒ is given by the complex number:

When s < sub > P </ sub >( t ), is expressed as a periodic summation of another function, s ( t ):

When s < sub > N </ sub > is expressed as a periodic summation of another function: and

When a ligand activates the G protein-coupled receptor, it induces a conformational change in the receptor that allows the receptor to function as a guanine nucleotide exchange factor ( GEF ) that exchanges GDP for GTP on the G < sub > α </ sub > subunit.

When storing records in a large unsorted file, one may use a hash function to map each record to an index into a table T, and collect in each bucket T a list of the numbers of all records with the same hash value i. Once the table is complete, any two duplicate records will end up in the same bucket.

When testing a hash function, the uniformity of the distribution of hash values can be evaluated by the chi-squared test.

When this approach is used, the hash function must be chosen so that the result has fairly uniform distribution between 0 and n − 1, for any value of n that may occur in the application.

When the hash function is used to store values in a hash table that outlives the run of the program, and the hash table needs to be expanded or shrunk, the hash table is referred to as a dynamic hash table.

When the result sequence is exhausted ( e. g. there are no more values within the result sequence ), the expression or function fails.

When one is found, and the position is odd, the location is returned from the function with suspend.

When the loop is closed, the system may function as an artificial pancreas.

When using codomains, the inverse of a function is required to have domain Y and codomain X.

When team members individually and collectively commit to team goals, team effectiveness is increased and is a function of increased supportive team behaviors ( Aube & Rousseau, 2005 ).

When renal function, measured by glomerular filtration rate, is persistently poor, dialysis and kidney transplantation may be treatment options.

When, for example, we use a verb to function as the action done by a subject, many languages require conjugating the verb to reflect that meaning.

When they react with monoamine oxidase, they permanently deactivate it, and the enzyme cannot function until it has been replaced by the body, which can take about two weeks.

When is a conditional probability distribution and the loss function is the negative log likelihood:, then empirical risk minimization is equivalent to maximum likelihood estimation.

When dealing with general function R → C, the transform takes on an integral form:

When left untreated, complications of PKU include severe mental retardation, brain function abnormalities, microcephaly, mood disorders, irregular motor functioning, and behavioral problems such as attention deficit hyperactivity disorder.

When the function is used as in