When using the Laplace transform in circuit analysis, the impedance of an ideal inductor with no initial current is represented in the s domain by:

When the manifold is Euclidean space, the Laplace operator is often denoted as ∇< sup > 2 </ sup > and so Poisson's equation is frequently written as

When Laplace came back a few days later, d ' Alembert was even less friendly and did not hide his opinion that it was impossible that Laplace could have read and understood the book.

When the transfer function and the Laplace transform of the input are known, this convolution may be more complicated than the alternative of multiplying two functions in the frequency domain.

Bruce Hindmarsh suggests that the secular popularity of " Amazing Grace " is due to the absence of any mention of God in the lyrics until the fourth verse ( by Excell's version, the fourth verse begins " When we've been there ten thousand years "), and that the song represents the ability of humanity to transform itself instead of a transformation taking place at the hands of God.

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

When the coordinates are transformed, for example by rotation or stretching, then the components of the vector also transform.

When the <- ως > ending is used to transform an adjective whose tonal accent is on the third syllable from the end, such as < επίσημος > (< epísimos >, " official "), the corresponding adjective is accented on the second syllable from the end ; compare < επίσημα > (< epísima >) and < επισήμως > (< episímos >), which both mean " officially ".

When the independent variable x represents time ( with SI unit of seconds ), the transform variable ξ represents frequency ( in hertz ).

When forced to rely on an implied license, a hiring party often finds that it has only limited rights to alter, update, or transform the work for which it paid.

For example, a Givens rotation affects only two rows of a matrix it multiplies, changing a full multiplication of order n < sup > 3 </ sup > to a much more efficient order n. When uses of these reflections and rotations introduce zeros in a matrix, the space vacated is enough to store sufficient data to reproduce the transform, and to do so robustly.

When the builders began to transform the mastaba into the four step pyramid, they made a major shift in construction.

When the living tree doctrine is applied right, the authors claim, " The elm remained an elm ; it grew new branches but did not transform itself into an oak or a willow.

When the situation becomes desperate, Shin Hayata, the Patrol's most capable member, holds the key to salvation in the form of the " Beta Capsule ," which, when activated, allows him to transform secretly into the super-humanoid-powered giant from space, who becomes known to the people of Earth as Ultraman.

When the series converges absolutely, is the discrete-time Fourier transform of the sequence a < sub > 0 </ sub >, a < sub > 1 </ sub >, ....

When applying a transform to a surface it is sometimes convenient to derive normals for the

When the psychoacoustic model is inaccurate, when the transform block size is restrained, or when aggressive compression is used, this may result in compression artifacts.

When he finds an anthill with a bird on it, he must say a certain phrase, which causes the bird to transform into a small person.

When a Chao begins to grow up, it will eventually go into a cocoon stage in which it will transform.

: When Romio arrives on the scene to help Ramia after Pixy Misa's defeat, she takes control of Eimi and causes her to transform into her own champion magical girl,.

When a light wave of a given frequency strikes a material with particles having the same or ( resonant ) vibrational frequencies, then those particles will absorb the energy of the light wave and transform it into thermal energy of vibrational motion.

When she was a baby, a servant claimed to have seen her face transform into a rose.

When he had fixed the camera, a hearse happened to be passing by just as Méliès restarted rolling the film, his end result was that he had managed to make a bus transform into a hearse, which is a camera effect called a stop trick.

When the screen scrolls up under " up " key press, the transform is active, and passive otherwise.

When word of Alpha Red got out, Vergere was able to infiltrate security and use the chemical compounds she manufactured through the Force, residing in her system, to transform Alpha Red into something harmless.

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.