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For each K, the function E < sub > K </ sub >( P ) is required to be an invertible mapping on
Some Related Sentences
For and each
For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.
For centuries the North Atlantic nations dominated the world and as long as they did they could afford the luxury of fighting each other.
For instance -- what about all those people Harold Rhodes went toward unhesitatingly, as if this were the one moment they would ever have together, their one chance of knowing each other??
For each State ( except Puerto Rico, Guam, the Virgin Islands, and, prior to 1962, Alaska and Hawaii ) determine average per capita income based on the last three years.
( For each State, make all computations set forth in items 1 to 8 above, and then add the results obtained for each State in item 8.
For each State ( except the Virgin Islands, Guam, Puerto Rico, and, prior to 1962, Alaska and Hawaii ), determine the average per capita income for the last three years.
For the year 2000 this means servicing ( A ) the protection requirements of a watershed producing at least 200 million acre-feet of water each year, ( B ) recreation and wildlife resources used each year by 635 million visitors, ( C ) a timber resource supporting an annual cut of 21 billion board feet, and ( D ) 60 million acres of rangelands.
Moreland fixed us each another drink, and said, `` For God's sake, tell me something truly amusing ''.
For an experiment to qualify as a binomial experiment, it must have four properties: ( 1 ) there must be a fixed number of trials, ( 2 ) each trial must result in a `` success '' or a `` failure '' ( a binomial trial ), ( 3 ) all trials must have identical probabilities of success, ( 4 ) the trials must be independent of each other.
For each of these lines meets Q in three points, namely two points on **zg and one point on one of the multiple secants.
For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.
The Wechsler Intelligence Scale For Children was administered to each sample third-grade child by a clinical worker.
For example, one hebephrenic man used to annoy me, month after month, by saying, whenever I got up to leave and made my fairly steoreotyped comment that I would be seeing him on the following day, or whenever, `` You're welcome '', in a notably condescending fashion -- as though it were his due for me to thank him for the privilege of spending the hour with him, and he were thus pointing up my failure to utter a humbly grateful, `` thank you '' to him at the end of each session.
For easy viewing, the middle 2 beads on each wire ( the 5th and 6th bead ) usually are of a different colour from the other eight beads.
For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.
For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.
For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.
For any real number the absolute value or modulus of is denoted by ( a vertical bar on each side of the quantity ) and is defined as
For and K
For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.
For the specific heats at least, the limiting value itself is definitely zero, as borne out by experiments to below 10 K. Even the less detailed Einstein model shows this curious drop in specific heats.
For example the United States uses NTSC-M, the UK uses PAL-I, France uses SECAM-L, much of Western Europe and Australia uses PAL-B / G, most of Eastern Europe uses PAL-D / K or SECAM-D / K and so on.
For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension.
For a time, memory capacities were often expressed in K, even when M could have been used: The IBM System / 370 Model 158 brochure ( 1972 ) had the following: " Real storage capacity is available in 512K increments ranging from 512K to 2, 048K bytes.
For example, trace ( but detectable ) amounts of carbon-14 (< sup > 14 </ sup > C ) are continually produced in the atmosphere by cosmic rays impacting nitrogen atoms, and argon-40 (< sup > 40 </ sup > Ar ) is continually produced by the decay of primordially occurring but unstable potassium-40 (< sup > 40 </ sup > K ).
For the Sun and stars with low temperatures, the prominence of the H and K lines can be an indication of strong magnetic activity in the chromosphere.
For example, Philip K. Dick's works contain recurring themes of social decay, artificial intelligence, paranoia, and blurred lines between objective and subjective realities, and the influential cyberpunk movie Blade Runner is based on one of his books.
A fan of Philip K. Dick, author of " We Can Remember it For You Wholesale ," the short story upon which the film was based, Cronenberg related ( in the biography / overview of his work, Cronenberg on Cronenberg ) that his dissatisfaction with what he envisioned the film to be and what it ended up being pained him so greatly that for a time, he suffered a migraine just thinking about it, akin to a needle piercing his eye.
For instance, Freeze Arrows ( introduced in DDRMAX ) which is a long green arrow that must be held down until the tail of it reaches the Step Zone, that is given an " O. K .!
* K, the ring of polynomials over a field K. For each nonzero polynomial P, define f ( P ) to be the degree of P.
* K < nowiki ></ nowiki > X < nowiki ></ nowiki >, the ring of formal power series over the field K. For each nonzero power series P, define f ( P ) as the degree of the smallest power of X occurring in P. In particular, for two nonzero power series P and Q, f ( P )≤ f ( Q ) iff P divides Q.
For example, the K ' iche ' language spoken in Guatemala has the inflectional prefixes k-and x-to mark incompletive and completive aspect ; Mandarin Chinese has the aspect markers-le 了 ,-zhe 着, zài-在, and-guò 过 to mark the perfective, durative stative, durative progressive, and experiential aspects, and also marks aspect with adverbs ; and English marks the continuous aspect with the verb to be coupled with present participle and the perfect with the verb to have coupled with past participle.
For example, Q-Q-K-3-2 would win ( because its K kicker outranks the 10 ), but Q-Q-10-4-3 would lose ( because its 4 is outranked by the 5 ).
For example, assume that a Texas hold ' em board looks like this after the third round: 5 ♠ < font color = red > K ♦ 7 ♦</ font > J ♠, and that a player is holding < font color = red > A ♦ 10 ♦</ font >.
For example, in the Harry Potter novels, J. K. Rowling reshapes a standard English proverb into “ It ’ s no good crying over spilt potion ” and Dumbledore
For example, with K ♠- 9 ♠- 8 ♣- 7 ♠- 6 ♣- 5 ♠- 4 ♠ playing the flush would put 8-6 in front, playing the 9-high straight would put K-4 up front, but the correct play is K-9 and 8-7-6-5-4.
For the limit process, we use the restriction homomorphisms Gal ( F < sub > 1 </ sub >/ K ) → Gal ( F < sub > 2 </ sub >/ K ), where F < sub > 2 </ sub > ⊆ F < sub > 1 </ sub >.