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Page "Examples of differential equations" ¶ 19
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If and value
If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.
If she chose, and in that final decision discarded, what, above all, all of us value, life itself, must she not have risen to her fullest height, and transcending her murky self, felt at last the passion of a great moral decision??
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
If you move them toward the beam, you count their value.
If you move away, you don't count their value.
If an alpha channel is used in an image, it is common to also multiply the color by the alpha value, to save on additional multiplications during compositing.
If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero.
If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.
* If the operation is associative, ( ab ) c = a ( bc ), then the value depends only on the tuple ( a, b, c ).
* If the operation is commutative, ab = ba, then the value depends only on
If the hand value exceeds 21 points, it busts, and all bets on it are immediately forfeit.
* Split ( only available as first decision of a hand ): If the first two cards have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box of the original bet.
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If a node has fewer than two children, some of the child pointers may be set to a special null value, or to a special sentinel node.
If the opponent drops the doubled stakes, he loses the game at the current value of the doubling cube.
If a house or car is above a certain value, the bankrupt can buy the interest back from the estate in order to keep the asset.
If a mutual is large, or is expected to grow if it can raise capital by a conversion, its managers derive more value from a conversion but do not suffer much loss of perks than if the bank were small.
If the shooter " hits " the point value again ( any value of the dice that sum to the point will do ; the shooter doesn't have to exactly repeat the value combination of the come-out roll ) before rolling a seven, the Pass line wins and a new round starts, usually with the dice staying with the current shooter.
If the roll is any other value, it establishes a point ; if that point is rolled again before a seven, the bet wins.
If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
If its value is 127 and it is instructed to add one, the computer can not store the number 128 in that space.
If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.
If the rich man is to be saved, all he must do is to follow the two commandments, and while material wealth is of no value to God, it can be used to alleviate the suffering of our neighbor.

If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If and known
If he attaches little importance to personal liberty, why not make this known to the world??
If communications work, his decision would be instantly known in all command posts that would originate the actual go order.
If we consider a process in which the outcome of one stage is known before passage to the next, then the principle of optimality shows that the policy in subsequent stages should be optimal with respect to the outcome of the first.
I kept saying, `` If I could just build up a reputation for myself, make some real money, get to be well known as an illustrator -- like Peter Askington, for instance -- then I could take some time off and paint ''.
If sets of statistical moments are known:
If so, Alcuin's origins may lie in the southern part of what was formerly known as Deira.
If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.
Litigation for the purpose of profit is referred to as “ Ambulance chasing ”: If for the purpose of harassment, for example to silence critics, it is known as a strategic lawsuit against public participation ( SLAPP ).
If the heat of vaporization and the vapor pressure of a liquid at a certain temperature is known, the normal boiling point can be calculated by using the Clausius-Clapeyron equation thus:
If a newer system is attempting to achieve integration with an older system which has known flaws ( or " bugs "), then the new system may be referred to as " bugwards-compatible ".
If the convention B < sub > 1 </ sub >=− is used, this sequence is also known as the first Bernoulli numbers ( / in OEIS ); with the convention B < sub > 1 </ sub >=+ is known as the second Bernoulli numbers ( / in OEIS ).
If the algorithm is symmetric, the key must be known to the recipient and sender and to no one else.
If a similar dispute has been resolved in the past, the court is bound to follow the reasoning used in the prior decision ( this principle is known as stare decisis ).
If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by
If organized as a division then the top manager is often known as an Executive Vice President ( for example, Todd Bradley who heads the Personal Systems Group in Hewlett Packard ).
If that business is a subsidiary which has considerably more independence then the title might be known as Chairman and CEO ( for example, Philip I. Kent of Turner Broadcasting System in Time Warner ).
If the compiled program can run on a computer whose CPU or operating system is different from the one on which the compiler runs, the compiler is known as a cross-compiler.
If the come-out roll is 2, 3 or 12, the bet loses ( known as " crapping out ").
If the grade is known, then the rate of ascent can be calculated using trigonometry.
If a " positive list " approach were taken, only species evaluated and approved for the positive list would be permitted in trade, thus lightening the review burden for member states and the Secretariat, and also preventing inadvertent legal trade threats to poorly known species.
If these structures are manipulated incorrectly, through processes known as chromosomal instability and translocation, the cell may undergo mitotic catastrophe and die, or it may unexpectedly evade apoptosis leading to the progression of cancer.
If later heat treatments cause this glass to become partly crystalline, the resulting material is known as a glass-ceramic, widely used as cooktop.
If the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution.

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