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If λ represents wavelength and f represents frequency ( note, λf = c where c is the speed of light ), then z is defined by the equations:
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If and λ
If λ < sub > 1 </ sub >, ..., λ < sub > ν </ sub > are the eigenvalues of J they will be resonant if one eigenvalue is an integer linear combination of two or more of the others.
# 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 A is a disjoint union of countably many disjoint Lebesgue measurable sets, then A is itself Lebesgue measurable and λ ( A ) is equal to the sum ( or infinite series ) of the measures of the involved measurable sets.
# If A and B are Lebesgue measurable and A is a subset of B, then λ ( A ) ≤ λ ( B ).
# If A is a Lebesgue measurable set with λ ( A ) = 0 ( a null set ), then every subset of A is also a null set.
If we do not alter the system, then the parameter λ is unchanged from measurement to measurement ; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase.
* If the base field is R, then for all real numbers λ.
* If the base field is C, then for all complex numbers λ, where denotes the complex conjugation of λ.
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 λ < sub > c </ sub > is the central wavelength, λ < sub > 0 </ sub > is the central wavelength at normal incidence, and n < sup >*</ sup > is the filter effective index of refraction, then:
If n is a positive integer, then λ ( n ) is defined as:
T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm λ x.
If a vector v of size n happens to be an eigenvector of A with eigenvalue λ, in other words if, then
If the system is in state ψ, then immediately after measurement the system will occupy a state which is an eigenvector e of A and the observed value λ will be the corresponding eigenvalue of the equation A e
No notation is used to describe the set of all λ, which satisfy this condition, but for a subset: If λ-T does not have dense range but is injective, λ is said to be in the residual spectrum of T, denoted by σ < sub > r </ sub >( T ).
If T is a compact operator, then it can be shown that any nonzero λ in the spectrum is an eigenvalue.
If α is a limit ordinal, an α-inaccessible is a fixed point of every ψ < sub > β </ sub > for β < α ( the value ψ < sub > α </ sub >( λ ) is the λ < sup > th </ sup > such cardinal ).
If and represents
If through lack of issue, marriage or both, eventually only one person represents the claims of all the sisters, he or she can claim the dignity as a matter of right, and the abeyance is said to be terminated.
If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.
If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.
If a party represents more than 4 states then such parties are considered as national parties.
If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.
If the Mythological Cycle represents a Golden Age, the Ulster Cycle is Ireland's Heroic Age.
If negation is cyclic and "∨" is a " max operator ", then the law can be expressed in the object language by ( P ∨ ~ P ∨ ~~ P ∨ ... ∨ ~...~ P ), where "~...~" represents n − 1 negation signs and "∨ ... ∨" n − 1 disjunction signs.
If the alphabet consists of alternative symbols, each symbol represents a message consisting of N bits.
If the secondary winding is made open-circuit, the current I < sub > 0 </ sub > taken by the magnetizing branch represents the transformer's no-load current.
If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event.
If the vector represents a directed distance or displacement from a point A to a point B ( see figure ), it can also be denoted as or < u > AB </ u >.
If the delta function is conceptualized as modeling an idealized point mass at 0, then δ ( A ) represents the mass contained in the set A.
If a signal is present, then this factor represents the decrease in signal to noise ratio incurred using the receiver system with a noise temperature of.
( If the object represents a static field then the parameter is ignored and may be.
( If the object represents a static method then the first parameter is ignored and may be.
If f represents a very small but intense source of heat, then the preceding integral can be approximated by the delta distribution, multiplied by the strength of the source.
) If the analemma is drawn in a diagram, tilted at the appropriate angle for an observer's latitude ( as described above ), and if a horizontal line is drawn to pass through the position of the Sun on the analemma on any given date ( interpolating between the date markings as necessary ), then at sunrise this line represents the horizon.
If the factor i were absent, the H matrix would be antihermitian and would have purely imaginary eigenvalues, which is not the traditional way quantum mechanics represents observable quantities like the energy.
If represents the number of dollars you have in chips after n tosses, with, then the sequence is a Markov process.
If represents the total value of the coins set on the table after n draws, with, then the sequence is not a Markov process.
Pettibon stated " If a white flag means surrender, a black flag represents anarchy.
If the number has a line above it, then it represents a unit fraction ( that is, would be ), whereas a line below the number indicates an integer.
If and wavelength
If more than one wavelength is present ( as is usually the case ), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.
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 the width of the slits is small enough ( less than the wavelength of the laser light ), the slits diffract the light into cylindrical waves.
If the width of the slits is greater than the wavelength, the Fraunhofer diffraction equation gives the intensity of the diffracted light as:
If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the light spectrum.
If the beam of light is not orthogonal ( or rather normal ) to the boundary, the change in wavelength results in a change in the direction of the beam.
If the pitch of this twist is on the order of the wavelength of visible light, then interesting optical interference effects can be observed.
If two waves of the same wavelength and frequency are in phase, both the wave crests and wave troughs align.
If the wavelength is much shorter than the target's size, the wave will bounce off in a way similar to the way light is reflected by a mirror.
If the wavelength is much longer than the size of the target, the target may not be visible because of poor reflection.
If the waves have the correct frequency ( or wavelength ) and polarization, their energy can be transferred to the charged particles in the plasma, which in turn collide with other plasma particles, thus increasing the temperature of the bulk plasma.
If each mode received an equal partition of energy, the short wavelength modes would consume all the energy.
If the surface is rough enough to create path-length differences exceeding one wavelength, giving rise to phase changes greater than 2π, the amplitude, and hence the intensity, of the resultant light varies randomly.
If a photographic plate or another 2-D optical sensor is located within the scattered light field without a lens, a speckle pattern is obtained whose characteristics depend on the geometry of the system and the wavelength of the laser.
If a particle were massive enough that its Compton wavelength and Schwarzschild radius were approximately equal, its dynamics would be strongly affected by quantum gravity.
If the source has a maximum overall dimension or aperture width ( D ) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D < sup > 2 </ sup >/( 4λ ), S > 1.
If photons of a particular wavelength are absorbed by matter, then when we observe light reflected from or transmitted through that matter, what we see is the complementary color, made up of the other visible wavelengths remaining.
If only a single atom of hydrogen were present, then only a single wavelength would be observed at a given instant.
If the wavelength of light far exceeds the particle dimensions, the particles can be treated as electric dipoles in an electric field.
If light of a fixed frequency / wavelength / color ( as from a laser ) is assumed, then the time-harmonic ( frequency-domain ) form of the optical field is given as:
If the wavelength of a quantum particle is short enough, atoms or their nuclei can serve as diffraction obstacles.
0.616 seconds.