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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 arity of the operators is fixed, the result is a syntax lacking parentheses or other brackets that can still be parsed without ambiguity.
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.

If and loop
If f: X → Y morphism of pointed spaces, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.
If f: X → Y is a continuous map, x < sub > 0 </ sub > ∈ X and y < sub > 0 </ sub > ∈ Y with f ( x < sub > 0 </ sub >) = y < sub > 0 </ sub >, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.
If the painter encounters the mark but is going in a different direction, then some sort of loop has occurred which caused the painter to return to the mark.
If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring.
If Good Times was not stopped in time, an infected computer would enter an " nth-complexity infinite binary loop " ( a meaningless term ), damaging the processor.
If the manifold is a circle these are called loop groups, and have central extensions whose Lie algebras are ( more or less ) Kac – Moody algebras.
If there were no holes then a loop of rope kept the oars in place.
If i > n, then exit the loop.
If A = x, then exit the loop.
If i ≤ 0, then exit the loop.
If A = x, then exit the loop.
One can use that instruction, which is usually faster than a comparison against some arbitrary value ( requiring a subtraction ), to implement the command " If i ≤ 0, then exit the loop ".
If the feedback network is made of components with relatively constant, stable values, the variability of the op-amp's open loop response does not seriously affect the circuit's performance.
For example, in a negative feedback loop, the transcription factor acts as its own repressor: If the transcription factor protein binds the DNA of its own gene, it will down-regulate the production of more of itself.
If the loop is made backwards so that the bitter end is on the bottom, the resulting knot will be sideways.
If the sides of the flattened loop are pulled away from each other, the flattened loop ends pull out of the half hitches and the knot falls apart, but if the free ends
If both have the working end passing over the standing line, slide the second loop underneath the first one.
If you made both loops with the working end under the standing line, slide the second loop over the first one.
; Loop-invariant code motion: If a quantity is computed inside a loop during every iteration, and its value is the same for each iteration, it can vastly improve efficiency to hoist it outside the loop and compute its value just once before the loop begins.
If the exit block is unreachable from the entry block, it indicates an infinite loop.

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