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where θ < sub > r, p </ sub > is the angle between r and p measured from r to p ; an important distinction because without it, the sign of the cross product would be meaningless.
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where and θ
functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).
On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.
where θ is the true angle SEE ′, is the apparent angle S ′ EE ′, and is the relative speed between the presumed fixed frame of reference ( such as heliocentric ) and the observer's one.
where θ ∈ T < sub > f ( x )</ sub >< sup >*</ sup > N and X < sub > x </ sub > ∈ T < sub > x </ sub > M.
Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis of a Cartesian coordinate system, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±, where b = a × tan ( θ ) and where θ is the angle between the transverse axis and either asymptote.
The contact angle, θ < sub > C </ sub >, is the angle formed by a liquid at the three-phase boundary where the liquid, gas, and solid intersect.
: where E is the energy, τ is magnitude of the torque, and θ is the angle moved ( in radians ).
where μ is the location parameter, θ represents additional parameters, and is a function of the additional parameters.
: where θ is the angle of inclination of the normal, and p is the length of the normal.
where A and θ < sub > 0 </ sub > are arbitrary constants.
where θ < sub > 1 </ sub > and θ < sub > 2 </ sub > are the angles of incidence of a ray crossing the interface between two media with refractive indices n < sub > 1 </ sub > and n < sub > 2 </ sub >.
where R is the distance to the particle, θ is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.
The standard convention ( r, θ, φ ) conflicts with the usual notation for the two-dimensional polar coordinates, where θ is often used for the azimuth.
where r is the distance from the axis of rotation to the particle, F is the magnitude of the force applied, and θ is the angle between the position and force vectors.
where E is the energy, τ is magnitude of the torque, and θ is the angle moved ( in radians ).
where W is work, τ is torque, and θ < sub > 1 </ sub > and θ < sub > 2 </ sub > represent ( respectively ) the initial and final angular positions of the body.
where ( r, θ, φ ) correspond to a spherical coordinate system.
where the numerical aperture is defined as for θ being the half-angle of the cone of rays accepted by the microscope objective.
where and <
He also offers a conversion table ( see Cohen, 1988, p. 283 ) for eta squared ( η < sup > 2 </ sup >) where 0. 0099 constitutes a small effect, 0. 0588 a medium effect and 0. 1379 a large effect.
Reactions of acids are often generalized in the form HA H < sup >+</ sup > + A < sup >−</ sup >, where HA represents the acid and A < sup >−</ sup > is the conjugate base.
The numerical value of K < sub > a </ sub > is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid ( HA ) and the products are the conjugate base and H < sup >+</ sup >.
Because the range of possible values for K < sub > a </ sub > spans many orders of magnitude, a more manageable constant, pK < sub > a </ sub > is more frequently used, where pK < sub > a </ sub >
These nodes are areas where the action potential is amplified using a high density of sodium ( Na < big >+</ big >) ions and is subsequently passed along the axon.
Within a shell where n is some integer n < sub > 0 </ sub >, ranges across all ( integer ) values satisfying the relation.
It lacks the NH < sub > 2 </ sub > group because of the cyclization of the side-chain and is known as an imino acid ; it falls under the category of special structured amino acids .</ ref > where R is an organic substituent known as a " side-chain "); often the term " amino acid " is used to refer specifically to these.
½ ( pKa < sub > 1 </ sub > + pKa < sub > R </ sub >), where pKa < sub > R </ sub > is the side-chain pKa.
## < tt > SubBytes </ tt >— a non-linear substitution step where each byte is replaced with another according to a lookup table.
## < tt > ShiftRows </ tt >— a transposition step where each row of the state is shifted cyclically a certain number of steps.
The < tt > MixColumns </ tt > function takes four bytes as input and outputs four bytes, where each input byte affects all four output bytes.
where n < sup > c </ sup > denotes the charge conjugate state, i. e., the antiparticle.
where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.
where E < sub > 0 </ sub > is an infinite negative constant.
The Battle of Qarqar is mentioned in extra-biblical records, and was perhaps at Apamea where Shalmaneser III of Assyria fought a great confederation of princes from Cilicia, Northern Syria, Israel, Ammon, and the tribes of the Syrian desert ( 853 BC ), including Ahab ( A-ha-ab-bu < sup > mat </ sup >) ( Adad -' idri ).
where < big ></ big > is the number of degrees of freedom divided by two, R is the universal gas constant and n is the number of moles in the system ( a constant ).
We could, alternatively, choose an encoding for Turing machines, where an encoding is a function which associates to each Turing Machine M a bitstring < M >.
where and sub
where p is a program in L < sub > 2 </ sub >.
where and r
where r is the position vector of the particle relative to the origin, p is the linear momentum of the particle, and × denotes the cross product.
where is the component of p that is perpendicular to r. As above, the sign is decided based on the sense of rotation.
t < sub > r </ sub > * BW = 0. 35, where t < sub > r </ sub > is rise time in seconds and BW is bandwidth in Hz.
where n > 1 is an integer and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.
where n > m > 0 are integers and p, q, and r are prime numbers, then 2 < sup > n </ sup >× p × q and 2 < sup > n </ sup >× r are a pair of amicable numbers.
In 1996, Serge Vaudenay found a known-plaintext attack requiring 2 < sup > 8r + 1 </ sup > known plaintexts to break, where r is the number of rounds.
Driven off by Roman forces, the coalition host moved overland into Thracia, where finally it was crushed by emperor Claudius II ( r. 268-70 ) at Naissus ( 269 ).
The Hilbert space of a spin-0 point particle is spanned by a " position basis ", where the label r extends over the set of all points in space.
: The 2br enzymes, with the letter " r " denoting reduced binding to clavulanic acid and sulbactam, are also called inhibitor-resistant TEM-derivative enzymes ; nevertheless, they are commonly still susceptible to tazobactam, except where an amino acid replacement exists at position met69.
where h ( 0 ) is the height of the water at r
where r is the radius from the axis of rotation.
where h ( 0 ) is the height at r = 0 ( the axis ).
where r = radius of gyration of cross-section which is equal to the square root of ( I / A ), K = ratio of the longest half sine wave to the actual column length, and KL
( x ( s ), y ( s )) where s represents arc length and r is the position vector.
The tension at r is parallel to the curve at r and pulls the section to the right, so it may be written Tu =( Tcos φ, Tsin φ ), where T is the magnitude of the force and φ is the is the angle between the curve at r and the x-axis ( see tangential angle ).
Finally, weight of the chain is represented by ( 0, − λgs ) where λ is the mass per unit length, g is the acceleration of gravity and s is the length of chain between c and r.
0.262 seconds.