Given that the cost of replacing an executive can run over 100 % of his or her annual salary, any investment of time and energy in re-recruitment will likely pay for itself many times over if it helps a business retain just a handful of key players that would have otherwise left.

# Given an array of values to be sorted, set up an auxiliary array of initially empty " pigeonholes ," one pigeonhole for each key through the range of the original array.

" Given that science continually seeks to adjust its theories structurally to fit the facts, i. e., adjusts its maps to fit the territory, and thus advances more rapidly than any other field, he believed that the key to understanding sanity would be found in the study of the methods of science ( and the study of structure as revealed by science ).

Given this sense of caution among key members of the British cabinet and of the army, it is even harder to understand why the British government went against the advice of its generals ( such as Wolsely ) to send substantial reinforcements to South Africa before war broke out.

Given its location, Perth was perfectly placed to become a key transport centre with the coming of the railways, and its first station was built in 1848.

Given that SAD impacts a wide variety of occupational performance areas in a person ’ s life as described in the aforementioned section, occupational therapists ( OTs ) play a key role in helping individuals cope with SAD.

Given key responsibilities for the country's diplomacy in the Napoleonic Wars, he was responsible for planning the attack on Copenhagen in September 1807, much of which he undertook at his country estate, South Hill Park at Easthampstead in Berkshire.

Given the statement, " All of Peters friends either like to dance or like to go to the beach ", we can identify key aspects and rewrite using symbols including quantifiers.

She also had a small role as a call girl hired by Al Pacino's character in Oliver Stone's sports drama Any Given Sunday, as well as a key supporting role in Woody Allen's The Curse of the Jade Scorpion.

Given that the Ashuruballit I synchronism with Akhenaten has become the crucial link between Egyptian and Mesopotamian history in recent years, this issue is a key area of focus and dispute.

Given that John the Baptist was executed before the defeat of Herod by Aretas IV of Nabatea in the AD 36, and based on the scholarly estimates for the approximate date of the marriage of Herod Antipas and Herodias AD 28-35, Josephus establishes a key connection between the time frame of the ministry of Jesus and his execution.

Given the master public key, any party can compute a public key corresponding to the identity ID by combining the master public key with the identity value.

Given the global responsibilities of U. N. C. L. E., communications is a key supportive function.

Given a relation of order N, consider a projection that subtends X, Y, and Z as the key and W as the residual attribute.

Given a major key tonic ( I ), the related keys are:

Given a key, determining the-st hash location is computed by:

Given natural protection by its very steep slopes, the walls and bastions were constructed at only key places ; it has two gates – the Kalyan Darwaza in the south-east and the Pune Darwaza in the north-east.

* Given the key to the city of Jacksonville by Mayor Tommy Hazouri in 1988

Given an input value x, the owner of the secret key SK can compute the function value y

Given the first n digits of Ω and a k ≤ n, the algorithm enumerates the domain of F until enough elements of the domain have been found so that the probability they represent is within 2 < sup >-( k + 1 )</ sup > of Ω.

# Primitive recursion operator: Given the k-ary function and k + 2-ary function:

# Minimisation operator: Given a ( k + 1 )- ary total function:

Given a system of n-dimensional variables ( physical variables ), in k ( physical ) dimensions, write the dimensional matrix M, whose rows are the dimensions and whose columns are the variables: the ( i, j ) th entry is the power of the ith unit in the jth variable.

Given two C < sup > k </ sup >- vector fields V, W defined on S and a real valued C < sup > k </ sup >- function f defined on S, the two operations scalar multiplication and vector addition

Given two variables x and y, y is directly proportional to x ( x and y vary directly, or x and y are in direct variation ) if there is a non-zero constant k such that

Given a tensor a with rank q and dimensions ( i < sub > 1 </ sub >, ..., i < sub > q </ sub >), and a tensor b with rank r and dimensions ( j < sub > 1 </ sub >, ..., j < sub > r </ sub >), their outer product c has rank q + r and dimensions ( k < sub > 1 </ sub >, ..., k < sub > q + r </ sub >) which are the i dimensions followed by the j dimensions.

* Given any morphism k ′: K ′ → X such that f k ′ is the zero morphism, there is a unique morphism u: K ′ → K such that k u

Given an integer k, one defines the residue class of an integer n as the set of all integers congruent to n modulo k:

Given a spline S of degree n with k knots x < sub > i </ sub > we can write the spline as a Bézier spline as:

Given a set of k + 1 data points

Given a set of k + 1 data points

Given a circle k, with a center O, and a point P outside of the circle, we want to construct the ( red ) tangent ( s ) to k that pass through P. Suppose the ( as yet unknown ) tangent t touches the circle in the point T. From symmetry, it is clear that the radius OT is orthogonal to the tangent.

Given a field k, various kinds of closures of k may be introduced.

* Given a triangle OAB in which O is the center of a circle k, and points A ' and B ' inverses of A and B with respect to k, then

Given a homogeneous prime ideal P of, let X be a subset of P < sup > n </ sup >( k ) consisting of all roots of polynomials in P .< ref > The definition makes sense since if and only if for any nonzero λ in k .</ ref > Here we show X admits a structure of variety by showing locally it is an affine variety.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

Given a function f ∈ I < sub > x </ sub > ( a smooth function vanishing at x ) we can form the linear functional df < sub > x </ sub > as above.

) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.

Given two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.

Given f ∈ G ( x * x < sup >- 1 </ sup >, y * y < sup >-1 </ sup >) and g ∈ G ( y * y < sup >-1 </ sup >, z * z < sup >-1 </ sup >), their composite is defined as g * f ∈ G ( x * x < sup >-1 </ sup >, z * z < sup >-1 </ sup >).

Given a field K, the corresponding general linear groupoid GL < sub >*</ sub >( K ) consists of all invertible matrices whose entries range over K. Matrix multiplication interprets composition.

Given a topological space X, let G < sub > 0 </ sub > be the set X.

Given a complex-valued function ƒ of a single complex variable, the derivative of ƒ at a point z < sub > 0 </ sub > in its domain is defined by the limit

Given a polynomial of degree with zeros < math > z_n < z_

Given a ( random ) sample the relation between the observations Y < sub > i </ sub > and the independent variables X < sub > ij </ sub > is formulated as