According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

When b = 0, the eigenvalues of A determine the structure of the phase space.

" Linda " b / w " When I Learn How to Cry " ( Liberty 55531 )-BB No. 28, CB No. 26-( JB )

" Sidewalk Surfin '" b / w " When It's Over " ( Liberty 55727 )-BB No. 25, CB No. 28-( JB )

When integrated over the radius, this implies that for b = 1, the total number of stars is proportional to r < sup > 2 </ sup >.

To see this, the three corresponding normal vectors of the corner's perpendicular sides can be considered to form a basis ( a rectangular coordinate system ) ( x, y, z ) in which to represent the direction of an arbitrary incoming ray, b, c. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to-a while the y and z components are unchanged, resulting in a direction of b, c. Similarly, when reflected from side y and finally from side z, the b and c components are reversed.

Exponentiation is a mathematical operation, written as b < sup > n </ sup >, involving two numbers, the base b and the exponent ( or index or power ) n. When n is a positive integer, exponentiation corresponds to repeated multiplication ; in other words, a product of n factors, each of which is equal to b ( the product itself can also be called power ):

* Finale at JFK Stadium: a ) Bob Dylan, Keith Richards and Ronnie Wood – " Ballad of Hollis Brown ", " When the Ship Comes In ", Blowin ' In The Wind " ( JFK 03: 39 ), b ) USA for Africa ( led by Lionel Richie ) – " We Are the World " ( JFK 3: 55 )

When there is sufficient sunlight for it to feed by phototrophy, it uses chloroplasts containing the pigments Chlorophyll a and Chlorophyll b to produce sugars by photosynthesis.

From 2. 30pm on December 22, 1955 Burke made his first recordings for Apollo Records, six songs, in their studios at 457 West 45th Street, Manhattan, debuting with his own song " Christmas Presents " b / w " When I'm All Alone " ( Apollo 485 ), which debuted on DEcember 24, 1955 and became a minor hit.

This dust is then transported inward past the orbit of Epsilon Eridani b. When collisions between the dust grains are taken into account, the dust will reproduce the observed infrared spectrum and brightness.

When the coefficients a, b, and c, are real or complex, the roots are

If there exist one or more eigenvalues, then if the corresponding b < sub > i </ sub > ≠ 0, it is a paraboloid ( either elliptic or hyperbolic ); if the corresponding, the dimension i degenerates and does not get into play, and the geometric meaning will be determined by other eigenvalues and other components of b. When it is a paraboloid, whether it is elliptic or hyperbolic is determined by whether all other non-zero eigenvalues are of the same sign: if they are, then it is elliptic ; otherwise, it is hyperbolic.

b. When did the person come to the United States to stay?

b. When did this person come the United States to stay?

When he died without sons in 1898 the viscounty became extinct, but the barony descended to his brother Debonnaire John ( 1830 – 1900 ), whose son Augustus Debonnaire John ( b. 1868 ) became 9th Baron Monson in 1900.

When the emitter surface is clean, this FEM image is characteristic of: ( a ) the material from which the emitter is made: ( b ) the orientation of the material relative to the needle / wire axis ; and ( c ) to some extent, the shape of the emitter endform.

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 speaking about the reals, sometimes it means " all reals but a set of Lebesgue measure zero " ( formally, almost everywhere ).

When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state ; in simple terms, it is the possibility of a risk-free profit at zero cost.

When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

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.

When this is done, the model radius still decreases with mass, but becomes zero at M < sub > limit </ sub >.

When the angular velocity of this co-rotating frame is not constant, that is, for non-circular orbits, other fictitious forces — the Coriolis force and the Euler force — will arise, but can be ignored since they will cancel each other, yielding a net zero acceleration transverse to the moving radial vector, as required by the starting assumption that the vector co-rotates with the planet.

When a binary mixture is evaporated and the other component, e. g. a salt, has zero partial pressure for practical purposes, the process is simpler and is called evaporation in engineering.

When waves are added together, their sum is determined by the relative phases as well as the amplitudes of the individual waves so that the summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes.

When the two waves are in phase, i. e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i. e. the path difference is equal to half a wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero.

When investors and managers perform DCF analysis, the important thing is that the net present value of the decision after discounting all future cash flows at least be positive ( more than zero ).

When a third variable is involved and has not been controlled for, the relation is said to be a zero order relationship.

When the exponent is zero, the result is always 1 ( e. g. is always rewritten to ).

When such a system is subject to an impulse ( or any signal of finite duration ) it will respond with an output waveform which lasts past the duration of the input, eventually decaying exponentially in one or another manner, but never completely settling to zero ( mathematically speaking ).

When a system, for example, n moles of a gas of volume V at pressure p and temperature T, is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy U plus pV, where pV is the work done in pushing against the ambient ( atmospheric ) pressure.

When there is no flow, there is no lift and the aerodynamic forces acting on the airfoil are zero.

When distinguishing between these zero references, the following terms are used:

When indicated, the zero reference is stated in parenthesis following the unit, for example 101 kPa ( abs ).

When n = 0, does not have zero elements ; rather, it is isomorphic to, since.

When the function's argument is 0 ( zero ) it will return the integer 1 ( one ).

When spring training concluded, Smith had amassed a. 288 batting average and zero errors in the field, and Clayton batted. 190 with eight errors.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.