Help


[permalink] [id link]
+
Page "Inverse function" ¶ 14
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

If and domain
If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.
If the author wished, he could apply for a second 14 ‑ year monopoly grant, but after that the work entered the public domain, so it could be used and built upon by others.
If the author has been dead more than 70 years, the work is in the public domain in most, but not all, countries.
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.
If the name given in the delegation is a subdomain of the domain for which the delegation is being provided, there is a circular dependency.
If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.
If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.
If the domain consists of the non-negative numbers, then the function is injective and invertible.
If ƒ is an invertible function with domain X and range Y, then
If one assumed that magnetopause was just a boundary between a magnetic field in a vacuum and a plasma with a weak magnetic field embedded in it, then the magnetopause would be defined by electrons and ions penetrating one gyroradius into the magnetic field domain.
If R is commutative, then one can associate to every polynomial P in R, a polynomial function f with domain and range equal to R ( more generally one can take domain and range to be the same unital associative algebra over R ).
If R is an integral domain and f and g are polynomials in R, it is said that f divides g or f is a divisor of g if there exists a polynomial q in R such that f q = g. One can show that every zero gives rise to a linear divisor, or more formally, if f is a polynomial in R and r is an element of R such that f ( r ) = 0, then the polynomial ( X − r ) divides f. The converse is also true.
The key result is the structure theorem: If R is a principal ideal domain, and M is a finitely
If M is a free module over a principal ideal domain R, then every submodule of M is again free.
If Φ is a unital positive map, then for every normal element a in its domain, we have Φ ( a * a ) ≥ Φ ( a *) Φ ( a ) and Φ ( a * a ) ≥ Φ ( a ) Φ ( a *).
If the fully qualified domain name of any name server for a zone appears within that zone, the zone administrator provides IP addresses for that name server, which are installed in the parent zone as glue records ; otherwise, the delegation consists of the list of NS records for that zone.
If in addition all of the elements in the codomain are in fact mapped to by some element of the domain, then the function is said to be bijective ( see figures ).
* If the domain X = ∅ or X has only one element, the function is always injective.
The Gaussian integers form a principal ideal domain with units 1, − 1, i, and − i. If x is a Gaussian integer, the four numbers x, ix,x, and − ix are called the associates of x.
If the waveform is digitally created directly in the time domain using a non-bandlimited form, such as y = x-floor ( x ), infinite harmonics are sampled and the resulting tone contains aliasing distortion.
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 f is differentiable at every point in some domain, then the gradient is a vector-valued function ∇ f which takes the point a to the vector ∇ f ( a ).

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 real
If competition beats you to it, this exciting new product era can have real headaches in store.
If the photographically realistic continuity of dreams, however bizarre their combinations, denies that it is purely a composition of the brain, it must be compounded from views of diverse realities, although some of them may never be encountered in what we are pleased to call the real life.
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 one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.
Existence is the principle that gives reality to an essence not the same in any way as the existence: " If things having essences are real, and it is not of their essence to be, then the reality of these things must be found in some principle other than ( really distinct from ) their essence.
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 X is a real Banach space, then the polarization identity is
If A is a self-adjoint operator, then is always a real number ( not complex ).
If the Czech ethnic origin was to be stressed, combinations like " Bohemian of Bohemian language "( Čech českého jazyka ), " a real Bohemian " ( pravý Čech ) etc.
If the exponent r is even, then the inequality is valid for all real numbers x.
If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.
If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.
If the eigenvalues are all positive, then the frequencies are all real and the stationary point is a local minimum.
If zeal for orthodoxy caused him to overstep the limits of discretion, his real attitude towards Rome is sufficiently clear.
If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).
If this limit exists, then it may be computed by taking the limit as h → 0 along the real axis or imaginary axis ; in either case it should give the same result.
If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.
If a DBMS system responses users ' request in a given time period, it can be regarded as a real time database.
If the matrix entries are real numbers, the matrix can be used to represent two linear mappings: one that maps the standard basis vectors to the rows of, and one that maps them to the columns of.
If this operation has to be done in real time video games there is an easy trick to boost performance.
* If we think of as the set of real numbers, then the direct product is precisely just the cartesian product,.
* If we think of as the group of real numbers under addition, then the direct product still consists of.
* If we think of as the ring of real numbers, then the direct product again consists of.
The best known example is the ring of quaternions H. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring.

0.159 seconds.