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.

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.

The expression 0 < sup > 0 </ sup > has to be interpreted as 1.

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

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.

Hence the expression praeteriti senatores (" senators passed over ") is equivalent to e senatu ejecti ( those removed from the senate ).</ br > In some cases, however, the censors did not acquiesce to this simple mode of proceeding, but addressed the senator whom they had noted, and publicly reprimanded him for his conduct.

The final expression follows from the previous one by the symmetry of x and y in the first expression, and by comparison it follows that the sequence of binomial coefficients in the formula is symmetrical.

where each x is a variable or a negation of a variable, and each variable can appear multiple times in the expression.

In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

( The above expression is read as " the derivative of y with respect to x ", " d y by d x ", or " d y over d x ".

In such a case, one should say: ( x + 1 )< sup > 3 </ sup > is a polynomial expression which may be expanded or rewritten into the polynomial x < sup > 3 </ sup > + 3x < sup > 2 </ sup > + 3x + 1.

The expression 1 /( x < sup > 2 </ sup > + 1 ) is not a polynomial because it includes division by a non-constant polynomial.

Production of cI leads to the binding of cI to the OR1 and OR2 sites in the P < sub > R </ sub > promoter, turning off cro and other early gene expression.

cI represses transcription from P < sub > L </ sub > and P < sub > R </ sub > while upregulating and controlling its own expression from P < sub > RM </ sub >.

Each morphism f has a unique source object a and target object b. The expression, would be verbally stated as " f is a morphism from a to b ". The expression — alternatively expressed as,, or — denotes the hom-class of all morphisms from a to b.

Remarkably this expression denotes the same operation independently of whether the symbol + is interpreted as inclusive or or exclusive or.

where R denotes the distance to the source point P and R ' denotes the distance to the reflected point P. A consequence of this expression for the Green's function is the Poisson integral formula.

If denotes the polarization vector of the wave exiting the waveplate, then this expression shows that the angle between and is − θ.

The expression fechten mit dem langen schwert (" fighting with the long sword ") in the German school of fencing denotes the style of fencing which uses both hands at the hilt ; fechten mit dem kurzen schwert (" fighting with the short sword ") is used of half-sword fighting, with one ( gloved ) hand gripping the blade.

More precisely, a citation is an abbreviated alphanumeric expression ( e. g. ) embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work for the purpose of acknowledging the relevance of the works of others to the topic of discussion at the spot where the citation appears.

( This expression above is simply, where denotes a fixed point combinator.

The expression denotes the moment when a television series loses its credibility due to predictable repetition or contrived extensions of its theme, usually as a result of the writers being unable to maintain its quality indefinitely.

where denotes the expression P in which all free occurrences of x have been replaced with expression E.

* Downward entailing, a linguistic expression that denotes a monotone decreasing function

where the expression on the left denotes the second partial derivatives of f in x and y, respectively.

Since then writers have variously said that an expression stands for, designates, refers to, or denotes its reference.

with the connection form and d the exterior derivative, or via the same expression in which is a gauge form for the gauge group of V. The scalar t is used here only as an indeterminate to generate the sum from the determinant, and I denotes the n × n identity matrix.

The entity, called bottom, denotes an expression which does not return a normal value, either because it loops endlessly or because it aborts due to an error such as division by zero.

The expression A < sub > μ </ sub > B < sup > μ </ sup > is shorthand for, and the μ in B < sup > μ </ sup > denotes an index, not a power.

Aporia or aporeia ( Ancient Greek:: impasse ; lack of resources ; puzzlement ; doubt ; confusion ) denotes in philosophy a philosophical puzzle or state of puzzlement and in rhetoric a rhetorically useful expression of doubt.

Short-circuit evaluation, minimal evaluation, or McCarthy evaluation denotes the semantics of some Boolean operators in some programming languages in which the second argument is only executed or evaluated if the first argument does not suffice to determine the value of the expression: when the first argument of the function evaluates to, the overall value must be ; and when the first argument of the function evaluates to, the overall value must be.

It is also akin to the expression " something confused and yet complete " ( huncheng 混成 ) found in the Daode jing 25, which denotes the state prior to the formation of the world where nothing is perceptible, but which nevertheless contains a cosmic seed.

It has been said that this expression has stemmed from economists, who describe everything economic as affecting everything else, trying to find an expression which denotes the farthest logical connection from their current economic focus, in a sort of butterfly effect.

A variable is an expression because it denotes a value in memory, so y + 6 is an expression.