for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

Here the expression has the value 1 if m = 0 and 0 otherwise ( Iverson bracket ).

The last expression shows that the difference quotient equals 6 + h when h ≠ 0 and is undefined when h

The disjunctive identity is 0, which is to say that OR-ing an expression with 0 will never change the value of the expression.

Equivalently, the determinant can be expressed as a sum of products of entries of the matrix where each product has n terms and the coefficient of each product is − 1 or 1 or 0 according to a given rule: it is a polynomial expression of the matrix entries.

0 and rearranging terms, one obtains an expression for ƒ ( 0 ).

where n is a natural number, the coefficients are elements of R, and X is a formal symbol, whose powers X < sup > i </ sup > are just placeholders for the corresponding coefficients a < sub > i </ sub >, so that the given formal expression is just a way to encode the sequence, where there is an n such that a < sub > i </ sub > = 0 for all i > n. Two polynomials sharing the same value of n are considered equal if and only if the sequences of their coefficients are equal ; furthermore any polynomial is equal to any polynomial with greater value of n obtained from it by adding terms in front whose coefficient is zero.

If the bias is small, we can let U − E ≈ φM in the expression for κ, where φM, the work function, gives the minimum energy needed to bring an electron from an occupied level, the highest of which is at the Fermi level ( for metals at T = 0 kelvins ), to vacuum level.

In contrast, if the index numbers count from 0, the expression becomes this:

The imaginary term j has also canceled out, making Z < sub > 0 </ sub > a real expression, and so is purely resistive.

For example, where the nominal level is 0 dBm, the expression 0 dBm TLP, or simply, 0TLP, is used.

Finally, the fractional part of 43 / 7 is the reciprocal of 7, so its approximation in this scheme, 7, is exact ( 7 / 1 = 7 + 0 / 1 ) and produces the exact expression for 415 / 93.

Clearly the original Arrhenius expression above corresponds to n = 0.

the first three terms respectively have the coefficients 7, − 3, and 1. 5 ( in the third term the variables are hidden ( raised to the 0 power ), so the coefficient is the term itself ; it is called the constant term or constant coefficient of this expression ).

for some integer, where are coefficients ; to allow this kind of expression in all cases one must allow introducing terms with 0 as coefficient.

is a valid s-expression, but not a valid Lisp program, since Lisp uses prefix notation and a floating point number ( here 1. 0 ) is not valid as an operation ( the first element of the expression ).

To solve this instance of the decision problem we must determine whether there is a truth value ( TRUE or FALSE ) we can assign to each of the variables ( x < sub > 1 </ sub > through x < sub > 4 </ sub >) such that the entire expression is TRUE.

To study the behavior of this expression as h tends to zero, expand k < sub > h </ sub >.

The expression a < sup > x </ sup > denotes the conjugate of a by x, defined as x < sup >− 1 </ sup > a x.

Substituting the derivative of u < sub > ρ </ sub > into the expression for velocity:

The transform is sometimes denoted by the symbol, as in or or < ref group =" note "> As a linear transformation on a finite-dimensional vector space, the DFT expression can also be written in terms of a DFT matrix ; when scaled appropriately it becomes a unitary matrix and the X < sub > k </ sub > can thus be viewed as coefficients of x in an orthonormal basis .</ ref >

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

The non-interactive Unix command grep was inspired by a common special uses of qed and later ed, where the command < tt > g / re / p </ tt > means globally search for the regular expression < TT > re </ TT > and print the lines containing it.

With this expression one can, in principle, determine the enthalpy if C < sub > p </ sub > and V are known as functions of p and T.

In this period the correct expression for kinetic energy, ½mv < sup > 2 </ sup >, and its relation to mechanical work became established.

However, the expression sin < sup >− 1 </ sup > x usually does not represent the multiplicative inverse to sin x, but the inverse of the sine function applied to x ( actually a partial inverse ; see below ).

However, this expression implies the ability to identify the particle with n < sub > 1 </ sub > as " particle 1 " and the particle with n < sub > 2 </ sub > as " particle 2 ".

Note that if n < sub > 1 </ sub > and n < sub > 2 </ sub > are the same, the antisymmetric expression gives zero, which cannot be a state vector as it cannot be normalized.

By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag D < sub > p </ sub > ( which includes induced drag in a 3D wing ).

For example in the following expression y is a bound variable and x is free: < tt > λy. x x y </ tt >.

In the following expression one single occurrence of x is bound by the second lambda: < tt > λx. y ( λx. z x )</ tt >

# Cro binds to OR3 preventing access to the P < sub > RM </ sub > promoter preventing expression of the cI gene.

O and P are responsible for initiating replication, and Q is another antiterminator which allows the expression of head, tail and lysis genes from P < sub > R ’</ sub >.

( 43 )</ sup > gives the following expression, based on the equation of state for an ideal Fermi gas:

:"< sup >†</ sup > We shall use the expression ' computable function ' to mean a function calculable by a machine, and let ' effectively calculable ' refer to the intuitive idea without particular identification with any one of these definitions.

Being healed has been described as a privilege of accepting Christ's redemption on the cross .< sup > p </ sup > Pentecostal writer Wilfred Graves, Jr. views the healing of the body as a physical expression of salvation.

In algebra, a number that is the multiplier of a variable or expression ( e. g. the 3 in 3xy < sup > 2 </ sup >) is called a coefficient.

Within the parenthesis itself is found the expression 2 < sup > 2 </ sup >.

The first ( and only ) expression we come across that is expressed with an exponent is 2 < sup > 2 </ sup >.

So the correct value for our original expression, 4 × 2 < sup > 2 </ sup > − ( 2 + 2 < sup > 2 </ sup >), is 10.