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Page "Partial differential equation" ¶ 106
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If and string
If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.
If P is a program which outputs a string x, then P is a description of x.
If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.
If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.
( If one string runs out of letters to compare, then it is deemed to come first ; for example, " cart " comes before " carthorse ".
If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).
If the open string is in tune, but sharp or flat when frets are pressed, the bridge saddle position can be adjusted with a screwdriver or hex key to remedy the problem.
If the spheres only appear to rotate ( that is, we are watching stationary spheres from a rotating frame ), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed.
# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.
# If V is a set of symbols or characters then V * is the set of all strings over symbols in V, including the empty string.
If you measure the three qubits, you will observe a three-bit string.
If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes ( one representing the ingoing string, and the other — the outgoing one ).
If each mass point has the mass, the tension of the string is, the separation between the mass points is and are the offset of these points from their equilibrium points ( i. e. their position on a straight line between the two attachment points of the string ) the vertical component of the force towards point is
If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations (), () and () or equivalently 200 coupled first order differential equations.
If the original string had several substrings that occurred often, then the transformed string will have several places where a single character is repeated multiple times in a row.
If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.
* If lead-acid batteries are used, all cells in the formerly good parallel strings will begin to sulfate due to the inability for them to be fully recharged, resulting in the storage capacity of these cells being permanently damaged, even if the damaged cell in the one degraded string is eventually discovered and replaced with a new one.
* Joel Spolsky ( for Apps Hungarian ): " If you read Simonyi's paper closely, what he was getting at was the same kind of naming convention as I used in my example above where we decided that meant " unsafe string " and meant " safe string.

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 stretched
If binding around a not fully convex, or square-edged object, arrange the knot so the overhand knot portion is stretched across a convex portion, or a corner, with the riding turn squarely on top of it.
If a membrane is stretched over a curve C that forms the boundary of a domain D in the plane, its vibrations are governed by the wave equation
* If a person is lying on his / her stomach with arms stretched in front and another person raises his / her arms about 2 feet off the ground and holds them there for approximately one minute, with the person on the ground having his / her eyes closed and head hanging, then slowly lowers the arms to the ground, it will feel as if the arms are going below the level of the rest of the body.
An intrinsic definition of the Gaussian curvature at a point P is the following: imagine an ant which is tied to P with a short thread of length r. She runs around P while the thread is completely stretched and measures the length C ( r ) of one complete trip around P. If the surface were flat, she would find C ( r ) = 2πr.
If they were too small, he stretched them to fit.
If some force is acting on the elastic cantilever ( for example because some molecule is being stretched between the surface and the tip ), this will deflect upward ( repulsive force ) or downward ( attractive force ).
If the definition of a term such as “ equality ” can be stretched to include a particular act or condition, then public support for that act or condition is likely to be stronger than it was previously.
If an arm is stretched the span of the hand corresponds to an angle of 18 to 20 °.
If done carefully, these can sometimes be stretched without breaking, but cracks around lettering on some drums is common.
If disturbed in the open, this crake will often run in a crouch for a short distance, with its neck stretched forward, then stand upright to watch the intruder.
If it is close, it will appear stretched out, as if it is very close to the viewer.
If vessels cannot be stretched into the scrotum, or are separated and cannot be reconnected, a testis will die and atrophy.
If the pericycle is superficial and the cortex is retained either the endodermis is stretched or crushed or it keeps pace with the expansion of the vascular cylinder by radial anticlinal divisions, the new walls developing Casparian strips in continuity with the old ones.
If pressure is applied to the muscles of the right lower abdomen ( or iliac fossa ) near a very irritated appendix, then the muscle fibers in that area will be stretched and will hurt.
If an individual's skin elasticity and vascularity allow, most piercings can be stretched far beyond their initial size.
If a paper is stretched in an in-plane direction it will expand in its thickness direction due to its network structure.
If it is desired to transform a square into a circle, cord of length half the diagonal the square is stretched from the centre to the east part of it lying outside the eastern side of the square ; with one-third the part lying outside added to the remainder the half diagonal, the circle is drawn.
If it gets wet at this stage it must be stretched again until dry, or it will revert to being a stiff piece of scraped rawhide.
If this happens, they clearly its long body and legs stretched as far as possible to get in touch with the vegetation or the substrate to come.
If these tissues are stretched or torn, and the joint is instabilized by the injury, new bone is produced to help to stabilize the joint.

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