where α > − 1, δ < sub > m, n </ sub > is the Kronecker delta, and u < sub > α, m </ sub > is the m-th zero of J < sub > α </ sub >( x ).

for α > − 1 / 2 and where δ is the Dirac delta function.

where E is the electric field and δ < sup > 3 </ sup > is the 3-dimensional delta function.

where δ is the Dirac delta function.

The Lindemann criterion states that melting occurs because of vibrational instability, e. g. crystals melt when the average amplitude of thermal vibrations of atoms is relatively high compared with interatomic distances, e. g. < δu < sup > 2 </ sup >> 1 / 2 > δ < sub > L </ sub > R < sub > s </ sub >, where δu is the atomic displacement, the Lindemann parameter δ < sub > L </ sub > ≈ 0. 20 ... 0. 25 and R < sub > s </ sub > is a half of the inter-atomic distance.

The RNA fragments are then removed by DNA polymerase I for prokaryotes or DNA polymerase δ for eukaryotes ( different mechanisms are used in eukaryotes and prokaryotes ) and new deoxyribonucleotides are added to fill the gaps where the RNA was present.

In virus species with reverse transcriptase lacking DNA-dependent DNA polymerase activity, creation of double-stranded DNA can possibly be done by host-encoded DNA polymerase δ, mistaking the viral DNA-RNA for a primer and synthesizing a double-stranded DNA by similar mechanism as in primer removal, where the newly synthesized DNA displaces the original RNA template.

where δ ( E < sub > ψ </ sub >– E < sub > χ </ sub >) restricts tunneling to occur only between electron levels with the same energy.

where μ < sub > α </ sub > and μ < sub > δ </ sub > are the components of proper motion in the R. A. and Declination, respectively, and δ is the Declination.

where λ is the wavelength of the waves that are focused for imaging, D the entrance pupil diameter of the imaging system, in the same units, and the angular resolution δ is in radians.

The δ < sup > 18 </ sup > O of coraline red algae provides a useful proxy of sea surface temperature at high latitudes, where many traditional techniques are limited.

Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima, where a local minimum x < sup >*</ sup > is defined as a point for which there exists some δ > 0 so that for all x such that

Carbon from this type of clathrate is isotopically heavier ( δ < sup > 13 </ sup > C is-29 to-57 ‰) and is thought to have migrated upwards from deep sediments, where methane was formed by thermal decomposition of organic matter.

where δ equals Rasalgheti's angular diameter in arcseconds, d < sub > R </ sub > the star's diameter in AU, and D < sub > R </ sub > the Distance from Earth in parsecs.

: An automaton is represented formally by a 5-tuple ( Q, Σ, δ, q < sub > 0 </ sub >, F ), where:

: A sequence of states q < sub > 0 </ sub >, q < sub > 1 </ sub >, q < sub > 2 </ sub >,...., q < sub > n </ sub >, where q < sub > i </ sub > ∈ Q such that q < sub > 0 </ sub > is the start state and q < sub > i </ sub > = δ ( q < sub > i-1 </ sub >, a < sub > i </ sub >) for 0 < i ≤ n, is a run of the automaton on an input word w

Since only the positions in space – time are being warped, not the fields, the Ψ are all zero and the X < sub > μ </ sub >< sup > ν </ sup > equal the Kronecker delta δ < sub > μ </ sub >< sup > ν </ sup >, where we have used μ instead of r for the index.

The EDM is defined through the shift in the energy of a state when it is put in an external electric field: Δe = d · E + E · δ · E, where d is called the EDM and δ, the induced dipole moment.

where Kronecker delta δ < sub > ij </ sub > is a piecewise function of variables and.

The associated charge density is Qδ ( r ), where δ ( r ) is the Dirac delta function.

where δ ( Greek lower case delta ) means a small change.

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.

functions as real combinations of spherical harmonics Y < sub > lm </ sub >( θ, φ ) ( where l and m are quantum numbers ).

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 p is a program in L < sub > 2 </ sub >.

In rectangular waveguides, rectangular mode numbers are designated by two suffix numbers attached to the mode type, such as TE < sub > mn </ sub >, where m is the number of half-wavelengths across the width of the waveguide and n is the number of half-wavelengths across the height of the waveguide.