If there are g ( E ) dE states with energy E to E + dE, then the Boltzmann distribution predicts a probability distribution for the energy:

If, by contrast they are in a trans configuration, then the stereoisomer is assigned an E or Entgegen configuration.

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

If E / F is a Galois extension, then Aut ( E / F ) is called the Galois group of ( the extension ) E over F, and is usually denoted by Gal ( E / F ).

If the cause of the crash is uncertain, this number is rendered as 48454C50, which stands for " HELP " in hexadecimal ASCII characters ( 48 = H, 45 = E, 4C = L, 50 = P ).

If M is an R module and is its ring of endomorphisms, then if and only if there is a unique idempotent e in E such that and.

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

A measure μ is monotonic: If E < sub > 1 </ sub > and E < sub > 2 </ sub > are measurable sets with E < sub > 1 </ sub > ⊆ E < sub > 2 </ sub > then

A measure μ is countably subadditive: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … is a countable sequence of sets in Σ, not necessarily disjoint, then

A measure μ is continuous from below: If E < sub > 1 </ sub >, E < sub > 2 </ sub >, E < sub > 3 </ sub >, … are measurable sets and E < sub > n </ sub > is a subset of E < sub > n + 1 </ sub > for all n, then the union of the sets E < sub > n </ sub > is measurable, and

If ΔS and / or T are small, the condition ΔG < 0 may imply that ΔH < 0, which would indicate an exothermic reaction.

If this article / noun pair is used as the object of a verb, it ( usually ) changes to the accusative case, which entails an article shift in German – Ich sehe den Wagen.

If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.

" If this is not an error for " ANaesthetic ", then it needs to be added as a noun sense to Wikipedia / Wiktionary?

If an ESN / MIN Pair is intercepted, it could then be cloned onto a different phone and used in other areas for making calls without paying.

If the rider is sitting upright, the rider's body creates about 75 % of the total drag of the bicycle / rider combination.

If the boat floats, the mass of the boat ( plus contents ) as a whole divided by the volume below the waterline is equal to the density of water ( 1 kg / l ).

If the book of Zephaniah was largely composed during the monarchic period, the author of the book of Zephaniah attempts to accomplish this change in behaviour through the threat of future calamity for “ those who have turned back from following the Lord, / who have not sought the Lord or inquired of him ” ( 1: 6 ).

If the convention B < sub > 1 </ sub >=− is used, this sequence is also known as the first Bernoulli numbers ( / in OEIS ); with the convention B < sub > 1 </ sub >=+ is known as the second Bernoulli numbers ( / in OEIS ).

If the slope / cliff being undercut is made of unconsolidated sediment it will erode at a much faster rate then a cliff made of bedrock.

If one key cannot be deduced from the other, the asymmetric key algorithm has the public / private key property and one of the keys may be made public without loss of confidentiality.

If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18 / 38 and his chance of losing 1 unit ( or winning-1 ) is 20 / 38.

If a 2, 000 ( lb / ac )/ year sequestration rate was achieved on all of cropland in the United States, nearly 1. 6 billion tons of carbon dioxide would be sequestered per year, mitigating close to one quarter of the country's total fossil fuel emissions.

If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained ( the best that is possible with a finite word length on the computer, and within the mathematical and / or physical approximations made ).

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

“ If you slaughter sheep, you will be considered guilty of a crime .” He issued a regulation to that effect ... 1279 / 1280 under Qubilai all the Muslims say: “ if someone else slaughters animal we do not eat ”.

If n ≥ 1 and is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation ; it is written as ( Z / nZ )< sup >×</ sup > or Z < sub > n </ sub >< sup >*</ sup >.

If a team places high enough at selected USASF / IASF sanctioned national competitions, they could be included in the Cheerleading Worlds and compete against teams from all over the world, as well as receive money for placing.

If a compression test does give a low figure, and it has been determined it is not due to intake valve closure / camshaft characteristics, then one can differentiate between the cause being valve / seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby effect the mentioned seal.

If " overseer " enzymes note that residues are misfolded, proteins within the RER will re-add glucose residues so that other Calreticulin / Calnexin can bind to these proteins and prevent them from proceeding to the Golgi.

If the bacterium senses that it is moving in the correct direction ( toward attractant / away from repellent ), it will keep swimming in a straight line for a longer time before tumbling.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If F ≥ F < sub > Critical </ sub > ( Numerator DF, Denominator DF, α )

If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.

If F is also surjective, then the Banach space X is called reflexive.

If F. tularensis were used as a weapon, the bacteria would likely be made airborne for exposure by inhalation.

If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

If F and G are ( covariant ) functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a morphism in D such that for every morphism in C, we have ; this means that the following diagram is commutative:

If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.

If certain coordinate systems are used, for instance, polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ × F will yield an incorrect result.

If φ is a scalar valued function and F is a vector field, then

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

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 vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).

If only layer C changes, we should find a way to avoid re-blending all of the layers when computing F. Without any special considerations, four full-image blends would need to occur.