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Page "Fourier transform" ¶ 9
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If and θ
If the orientation of the tangent relative to some starting position is θ ( s ), then ρ ( s ) is defined by the derivative dθ / ds:
If the parameter is denoted θ then the estimator is typically written by adding a " hat " over the symbol:.
* If θ < θ < sub > c </ sub >, the ray will split.
* If θ > θ < sub > c </ sub >, the entire ray reflects from the boundary.
If we suppose the screen is far enough from the slits ( that is, s is large compared to the slit separation d ) then the paths are nearly parallel, and the path difference is simply d sin θ.
If B is a circle, then these eigenfunctions have an angular component that is a trigonometric function of the polar angle θ, multiplied by a Bessel function ( of integer order ) of the radial component.
If scatterers are arranged symmetrically with a separation d, these spherical waves will be in sync ( add constructively ) only in directions where their path-length difference 2d sin θ equals an integer multiple of the wavelength λ.
If the flux j passes through the area at an angle θ to the area normal, then
If denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between and isθ.
If the probability density function is ƒ < sub > θ </ sub >( x ), then T is sufficient for θ if and only if functions g and h can be found such that
If X < sub > 1 </ sub >, ...., X < sub > n </ sub > are independent and uniformly distributed on the interval, then T ( X ) = max ( X < sub > 1 </ sub >, …, X < sub > n </ sub >) is sufficient for θthe sample maximum is a sufficient statistic for the population maximum.
If the mirror rotates at a known constant angular rate dθ / dt, the angle θ is given by:
If b is another such vector, and θ is the angle between them:
If only b is a unit vector, then the dot product a · b gives || a || cos θ, i. e., the magnitude of the projection of a in the direction of b, with a minus sign if the direction is opposite.
If 0 < e < 1, then the denominator of the equation of free orbits varies with the true anomaly θ, but remains positive, never becoming zero.
If G is a Lie group or an algebraic group, then a multiplicative character θ: G → F < sup >×</ sup > induces a weight χ
If a gauge transformation θ is applied to the electron waves, for example, then one must also apply a corresponding transformation to the potentials that describe the electromagnetic waves.
If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.
If η ( θ ) = θ, then the exponential family is said to be in canonical form.

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 measured
If the slowing down of certain seismic waves caused by the damp spot helped uncover the underground ocean, the unusual temperature variation with depth measured in 241 inactive oil wells helped locate the subterranean river.
where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.
* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then
If u ( t ) is the control signal sent to the system, y ( t ) is the measured output and r ( t ) is the desired output, and tracking error, a PID controller has the general form
If measured instead per unit wavelength, using Wien's law, the peak is at 1. 06 mm corresponding to a frequency of 283 GHz.
If it is the fraction of impinging atoms getting through the foil which is measured, the result can still be expressed in terms of the equivalent stopping cross section of the atoms.
If it is " observed " ( measured with a photon ) not at a particular slit but rather at the screen, then there is no " which path " information as part of the interaction, so the electron's " observed " position on the screen is determined strictly by its probability function.
If instead we use polar coordinates with the origin at one focus, with the angular coordinate still measured from the major axis, the ellipse's equation is
If the second electrode is also at standard conditions, then the measured cell potential is called the standard electrode potential for the electrode.
If these three home construction projects were measured with the same PV valuations, the relative schedule performance of the projects can be easily compared.
If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter.
If swelling is observed, the calf circumference should be measured with a tape measure.
If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid ( for example across an orifice plate or venturi ), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.
* If the measured value is contained in B, then immediately after the measurement, the system will be in the ( generally non-normalized ) state E < sub > A </ sub >( B ) ψ.
If the measured value does not lie in B, replace B by its complement for the above state.
If these relative frequencies are to define the probability, the probability will be slightly different every time it is measured.
If the objects are indeterminate until one of them is measured, then the question becomes, " How can one account for something that was at one point indefinite with regard to its spin ( or whatever is in this case the subject of investigation ) suddenly becoming definite in that regard even though no physical interaction with the second object occurred, and, if the two objects are sufficiently far separated, could not even have had the time needed for such an interaction to proceed from the first to the second object?
If, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero.
If, the magnetization will not flip during the measurement, so the measured magnetization will be what the instantaneous magnetization was at the beginning of the measurement.
* If it was an abortion, usually measured after three months in a pregnancy, the woman may pay 1 / 10 of the blood money to charity or face imprisonment ( not qisas ).
If the net force is not zero, and is the torque measured from, then the torque measured from is ...
If the rotational speed is measured in revolutions per unit of time, the linear speed and distance are increased proportionately by 2π in the above derivation to give:

0.135 seconds.