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If the arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that can still be parsed without ambiguity.
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If and arity
If a problem has constraints with a larger arity ( number of variables ), conversion into a problem made of binary constraints allows for execution of these solving algorithms.
If and operators
If X and Y are topological vector spaces, the space L ( X, Y ) of continuous linear operators f: X → Y may carry a variety of different possible topologies.
If the operators corresponding to two observables do not commute, they have no simultaneous eigenstates and they obey an uncertainty principle.
If not, the amateur operators were required to stop transmitting.
: If and are normal operators and if A is a bounded linear operator such that, then.
If X is a Hilbert space and T is a normal operator, then a remarkable result known as the spectral theorem gives an analogue of the diagonalisation theorem for normal finite-dimensional operators ( Hermitian matrices, for example ).
If one aircraft does not follow the directive ATC issues the directive will have to be reissued and in turn increase the workload of ATM operators.
If the Governor or the other officials of Idaho accept a cent from the operators or from any other capitalist with any reference, direct or indirect, to this prosecution, they would forfeit the respect of every good citizen and I should personally feel that they had committed a real crime.
If the gain was finally set to a 50 ° PB, then 80 % power will not be applied unless the furnace is 15 ° below setpoint, so for this other application the operators will have to remember always to set the setpoint temperature 15 ° higher than actually needed.
If the Lagrangian contains combinations of field operators of high enough dimension in energy units, the counterterms required to cancel all divergences proliferate to infinite number, and, at first glance, the theory would seem to gain an infinite number of free parameters and therefore lose all predictive power, becoming scientifically worthless.
If the parameters are considered as generalized coordinates, then should be identified as the generalized force operators related to those coordinates.
If the unperturbed system is in eigenstate at time, its state at subsequent times varies only by a phase ( we are following the Schrödinger picture, where state vectors evolve in time and operators are constant ):
If i is any inclusion of compact manifolds from X to Y, they defined a ' pushforward ' operation i < sub >!</ sub > on elliptic operators of X to elliptic operators of Y that preserves the index.
If D is a differential operator with adjoint D *, then D * D and DD * are self adjoint operators whose non-zero eigenvalues have the same multiplicities.
If the operators in the family are real, then the index lies in the real K-theory of Y.
If we specialize to categories arising from partially ordered sets ( with a single morphism from to iff ), then the formalism becomes much simpler: adjoint pairs are Galois connections and monads are closure operators.
If L is the Lie algebra corresponding to the Lie group G, U ( L ) can be identified with the algebra of left-invariant differential operators ( of all orders ) on G ; with L lying inside it as the left-invariant vector fields as first-order differential operators.
If an operator is left-associative, the operators are applied in left-to-right order.
If an operator is right-associative, the operators are applied in right-to-left order.
If an operand is both preceded and followed by operators ( for example, "^ 4 ^"), and those operators have equal precedence, then the operand may be used as input to two different operations ( i. e. the two operations indicated by the two operators ).
If a large magnet undergoes a quench, the inert vapor formed by the evaporating cryogenic fluid can present a significant asphyxiation hazard to operators by displacing breathable air.
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 fixed
If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.
If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.
If x is held fixed, then the Bessel functions are entire functions of α.
If A is a fixed element of a ring ℜ, the first additional relation can also be interpreted as a Leibniz rule for the map given by B ↦.
If G is a group, and g is a fixed element of G, then the conjugation map
If a rotating frame is chosen so that just the angular position of an object is held fixed, more complicated motion, such as elliptical and open orbits, appears because the centripetal and centrifugal forces will not balance.
If each pixel on the display actually contains three rectangular subpixels of red, green, and blue, in that fixed order, then things on the screen that are smaller than one full pixel in size can be rendered by lighting only one or two of the subpixels.
If a display does not have the type of fixed pixels that ClearType expects, text rendered with ClearType enabled actually looks worse than type rendered without it.
If someone sees something completely different than another, our language prevents us from acknowledging the other's point of view by limiting our perception to fixed states.
:" If a period fixed by weeks, months, and years does not commence from the beginning of a week, month, or year, it ends with the ending of the day which proceeds the day of the last week, month, or year which corresponds to that on which it began to commence.
Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.
If an equation can be put into the form f ( x ) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x < sub > 1 </ sub > in the basin of attraction of x, and let x < sub > n + 1 </ sub > = f ( x < sub > n </ sub >) for n ≥ 1, and the sequence
( If great wealth is not diluted, the positions in society tend to be much more fixed and opportunities to make an individual success are lower.
# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.
If two elements form more than one compound between them, then the ratios of the masses of the second element which combine with a fixed mass of the first element will be ratios of small whole numbers.
If the meteoroid maintains a fixed orientation for some time, without tumbling, it may develop a conical " nose cone " or " heat shield " shape.
If the revenue the firm is receiving is greater than its total variable cost ( R > VC ) then the firm is covering all variable cost plus there is additional revenue (" contribution "), which can be applied to fixed costs.
If the SEM is equipped with a cold stage for cryo-microscopy, cryofixation may be used and low-temperature scanning electron microscopy performed on the cryogenically fixed specimens.
At least two assumptions are necessary for the validity of the standard model: first, that supply and demand are independent ; and second, that supply is " constrained by a fixed resource "; If these conditions do not hold, then the Marshallian model cannot be sustained.
If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave.
If an inconsistency is encountered, the program can immediately halt, so that the bug can be located and fixed.
If the management ethos is to reward the number of bugs fixed, then some developers may quickly write sloppy code knowing they can fix the bugs later and be rewarded for it, whereas careful, perhaps " slower " developers do not get rewarded for the bugs that were never there.
If the waveform is a pure sine wave, the relationships between peak-to-peak, peak, mean, and RMS amplitudes are fixed and known, as they are for any continuous periodic wave.
If there is a fixed point, we can take that as the origin, and the affine transformation reduces to a linear transformation.
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