: When comparing the above illustration to the below text, please note that the above x: y aspect ratio values are shown as vertical orientation rectangles to better demonstrate visual differences, whereas the aspect ratio values of the text below are written as rotated horizontal orientation rectangles ( e. g. compare 3: 4 vertical orientation illustration to 4: 3 horizontal orientation text ).

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 a switch is pressed, it connects the corresponding x and y lines together.

When dealing with three or fewer variables, it is common to replace x < sub > 1 </ sub > with just x, x < sub > 2 </ sub > with y, and x < sub > 3 </ sub > with z, as appropriate.

When so pronounced, a modern transcription renders them all as < i >, but a transliteration still distinguishes them, for example by transliterating to < ē > < i > < y > and < ei > < oi > < yi >.

When viewed in this way the numbers x < sub > 1 </ sub >, ..., x < sub > n </ sub >, and y < sub > 1 </ sub >, ..., y < sub > n </ sub > are the components of x and y with respect to an orthonormal basis of V.

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.

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 she was nine years old, her father launched a vocal group consisting of several of his children, Selena y Los Dinos.

When the General Colonization Law went into effect in 1824, followed by the 1825 State Colonization Law of Coahuila y Tejas, Robert Leftwich obtained a grant to settle 800 families in Texas.

When the Spanish media asked King Juan Carlos if he would endorse the bill legalizing gay marriages, he answered " Soy el Rey de España y no el de Bélgica " (" I am the King of Spain, not of Belgium ")– a reference to King Baudouin I of Belgium, who had refused to sign the Belgian law legalising abortion.

When Enrique Zobel de Ayala ( 1877 – 1943 ), then a senior managing partner at Ayala y Cia.

When the media asked King Juan Carlos if he would endorse the 2005 bill legalizing gay marriages ( the implication implied that he may not endorse the bill ), he answered " Soy el Rey de España y no el de Bélgica " (" I am the King of Spain, not of Belgium ")– a reference to King Baudouin I of Belgium who had refused to sign the Belgian law legalising abortion in Belgium.

When the media asked King Juan Carlos if he would endorse the bill legalizing gay marriages, he answered " Soy el Rey de España y no el de Bélgica " (" I am the King of Spain, not of Belgium ") a reference to King Baudouin I of Belgium who had refused to sign the Belgian law legalising abortion.

When polynomial sequences replace sequences of numbers as images of y < sup > n </ sup > under the linear mapping L, then the umbral method is seen to be an essential component of Rota's general theory of special polynomials, and that theory is the umbral calculus by some more modern definitions of the term.

When R is the Beats-or-Ties binary relation on the set of candidates defined by x Beats-or-Ties y if and only if x pair-wise beats or ties y, then the resulting partial order is the beat-or-tie order which is a total order.

When we have an equation R ( x, y ) = 0, we may be able to solve it for y and then

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 this experiment is viewed as composed of five binomial trials, one for each member of the family, the outcomes of the trials are obviously not independent.

When Cyril ’ s bishop Maximus died Cyril was appointed bishop by Acasius of Caesaria, who was himself an Arian and viewed Cyril as a theological ally.

When Paul refers to Priscilla and Aquila, of the seven times Priscilla and Aquila are mentioned in the New Testament, the Apostle Paul always lists them together, suggesting that he viewed them as a ministry team and also a family unit.

When Cesare eventually took power, he was viewed by the citizens as a great improvement.

When Galileo was viewed as a private-sector development with public-sector financial participation, European Commission program managers sought Chinese participation in pursuit of Chinese cash in the short term and privileged access to China ’ s market for positioning and timing applications in the longer term.

When Spain tried to invade and conquer England it was a fiasco, and the defeat of the Spanish Armada in 1588 associated Elizabeth's name forever with what is popularly viewed as one of the greatest victories in English history.

When viewed by zoologists and professors of natural history it was concluded that it showed a seal, possibly a grey seal.

When viewed through a telescope or binoculars with no outside reference, it is difficult to judge the size of an object in the water.

When viewed under a microscope using a polarized light source, different liquid crystal phases will appear to have distinct textures.

" When the conservative web site the Drudge Report published this message, many Bush supporters viewed it as " smoking gun " evidence that Halperin was using ABC to propagandize against Bush to Kerry's benefit, by interfering with reporters ' attempts to avoid bias.

When viewed from " Viewpoint A ", the object appears to be in front of the blue square.

When viewed from directly in front, the speed may show exactly 60 ; but when viewed from the passenger seat the needle may appear to show a slightly different speed, due to the angle of viewing.

When one considers that rhetoric included torture ( it IS persuasive, and was accepted in forensics in the West until very recently ), it is clear that rhetoric cannot be viewed only in academic terms.

When his attempt to secure confirmation of Gaidar as prime minister was rejected, Yeltsin appointed Viktor Chernomyrdin, whom the parliament approved because he was viewed as more economically conservative than Gaidar.

When the cities are viewed as points in the plane, many natural distance functions are metrics, and so many natural instances of TSP satisfy this constraint.

When viewed through this formalism, the measurement of the wave function will randomly " collapse ", or rather " decohere ", to a sharply peaked function at some location.

When viewed from the side, such a layout appears as a " V " lying on its side.

" When rumors circulated that the top job would go to Marshall, many critics viewed the transfer as a demotion for Marshall, since he would leave his position as Chief of Staff of the Army and lose his seat on the Combined Chiefs of Staff.

When Henry died in 1125, Lothair was viewed by the imperial chancellor, the Archbishop of Mainz, as a perfect candidate.

When viewed edge-on, prominent dust-lanes are sometimes visible in absorption against the light of stars in the disk.

When the overhead map is viewed, some parts of certain levels have annotations that describe the name of an area.

When Spielberg and editor Michael Kahn viewed a rough cut of the film in late 1988, they felt it suffered from a lack of action.