When α is an integer, moreover, as was similarly the case for the functions of the first kind, the following relationship is valid:

When α is an integer, the Bessel functions J are entire functions of x.

When a ligand activates the G protein-coupled receptor, it induces a conformational change in the receptor that allows the receptor to function as a guanine nucleotide exchange factor ( GEF ) that exchanges GDP for GTP on the G < sub > α </ sub > subunit.

When perturbation theory is applied to quantum electrodynamics, the resulting perturbative expansions for physical results are expressed as sets of power series in α.

When α is very small ( α < π / 6 ), the following approximations can be done:

When viewed through a telescope, this system is resolved into two components designated α < sup > 1 </ sup > and α < sup > 2 </ sup >.

When P is chosen as the centroid G, then α = − 1 / 3.

When P is chosen as the circumcenter O, then α = − 1 and the generated orthocentric system is congruent to the original system as well as being a reflection of it about the nine-point center.

When both parameters are less than one ( α < 1 and β < 1 ), this is the anti-mode: the lowest point of the probability density curve.

When metarhodopsin activates transducin, the GDP bound to the α subunit ( T < sub > α </ sub >) is exchanged for GTP from the cytoplasm.

When I is a principal ideal αO < sub > K </ sub > then N ( I ) is equal to the absolute value of the norm to Q of α, for α an algebraic integer.

When the method of least squares is used to estimate α < sub > 0 </ sub > and α < sub > 1 </ sub >, then the residuals, unlike the errors, cannot be independent since they satisfy the two constraints

When the vector spaces involved are over the real numbers, a slightly more general form of homogeneity is often used, requiring only that () hold for all α > 0.

When prodynorphin is cleaved during processing by proprotein convertase 2 ( PC2 ), multiple active peptides are released: dynorphin A, dynorphin B, and α / β-neo-endorphin.

When the measure μ is associated to a mass distribution on a sufficiently smooth hypersurface S ( a Lyapunov surface of Hölder class C < sup > 1, α </ sup >) that divides R < sup > d </ sup > into two regions D < sub >+</ sub > and D < sub >−</ sub >, then the Newtonian potential of μ is referred to as a simple layer potential.

: When α = 1 / 2, the equation reduces to the Legendre equation, and the Gegenbauer polynomials reduce to the Legendre polynomials.

When there are only two means to compare, the t-test and the ANOVA F-test are equivalent ; the relation between ANOVA and t is given by F = t < sup > 2 </ sup >.

When the volume of an alcoholic drink is shown in centilitres, determining the number of units in a drink is as simple as < var > volume </ var > × < var > percentage </ var > ( converted into a fraction of 1 ).

( When measured in decibels it is logarithmically related to the power ratio: G ( dB )= 10 log ( P < sub > out </ sub > /( P < sub > in </ sub >)).

When fully implemented, CAIR will reduce SO < sub > 2 </ sub > emissions in 28 eastern states and the District of Columbia by over 70 percent and NOx emissions by over 60 percent from 2003 levels.

When clouds are present, the loss rate of SO < sub > 2 </ sub > is faster than can be explained by gas phase chemistry alone.

When certain ionic compounds containing bromine are mixed with potassium permanganate ( KMnO < sub > 4 </ sub >) and an acidic substance, they will form a pale brown cloud of bromine gas.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.

When the rate of bone formation exceeds the rate of bone resorption, soft tissue < sup > 44 </ sup > Ca /< sup > 40 </ sup > Ca rises.

When the partial pressure of is reduced, for example when a can of soda is opened, the equilibrium for each of the forms of carbonate ( carbonate, bicarbonate, carbon dioxide, and carbonic acid ) shifts until the concentration of in the solution is equal to the solubility of CO < sub > 2 </ sub > at that temperature and pressure.

When pH is too high, the concentration of hydrogen ions in the blood is too low, so the kidneys excrete bicarbonate ( HCO < sub > 3 </ sub >< sup >−</ sup >).

When applied to the simplest two-electron molecule, H < sub > 2 </ sub >, valence bond theory, even at the simplest Heitler-London approach, gives a much closer approximation to the bond energy, and it provides a much more accurate representation of the behavior of the electrons as chemical bonds are formed and broken.

When this is done, the model radius still decreases with mass, but becomes zero at M < sub > limit </ sub >.

When the critical stress, F < sub > cr </ sub > ( F < sub > cr </ sub > =

When Newton's method is used to find the solution for the maximum likelihood estimate, the middle 24 % order statistics can be used as an initial solution for x < sub > 0 </ sub >.

When s < sup > 2 </ sup >− v < sup > 2 </ sup > is expanded using these expressions the result is

When the trajectory r ( t ) rotates an amount dθ, u < sub > ρ </ sub >, which points in the same direction as r ( t ), also rotates by dθ.

When Yellowstone Caldera last erupted some 650, 000 years ago, it released about 1, 000 km < sup > 3 </ sup > of material ( as measured in dense rock equivalent ( DRE )), covering a substantial part of North America in up to two metres of debris.

* When the metal atoms are hexagonal close packed, ( hcp ), as the octahedral interstices lie directly opposite each other on either side of the layer of metal atoms, filling only one of these with carbon achieves 2: 1 stoichiometry with the CdI < sub > 2 </ sub > structure.

When the DNS resolver gets a PTR ( reverse-lookup ) request, it begins by querying the root servers ( which point to The American Registry For Internet Numbers ' ( ARIN's ) servers for the < tt > 208. in-addr. arpa </ tt > zone ).

When heavy metals or radionuclides form their own pure colloids, the term " Eigencolloid " is used to designate pure phases, e. g., Tc ( OH )< sub > 4 </ sub >, U ( OH )< sub > 4 </ sub >, Am ( OH )< sub > 3 </ sub >.

When Warhol was 13, his father died in an accident .< ref >

Cottard takes advantage of the crisis to make money by selling contraband cigarettes and inferior liquor .</ br > When the epidemic ends, Cottard's moods fluctuate.

However, years of activism, and fighting for the Republican side of the Spanish Civil War have left him disillusioned .</ br > When the plague epidemic is virtually over, Tarrou becomes one of its last victims, but puts up a heroic struggle before dying.

116 .</ ref > When air condenses it becomes visible, as mist and then rain and other forms of precipitation, and as the condensed air cools Anaximenes supposed that it went on to form earth and ultimately stones.