Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

) Let N be the ( possibly fractional ) number of submovements required to fall within the target.

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

Let us take the first example, where the target square is in the first row above the red line.

Let us imagine a spherical target ( in grey in the figure ) and a beam of particles ( in blue ) “ flying ” at speed v ( vector in black ) in the direction of the target.

*" Time Won't Let Me " b / w " Was It Really Real " – Capitol No. 5573, red and orange label with target logo

Let exactly 1'' '' of `` A '' extend beyond `` B '' and use a square to check your angle to exactly 90 degrees.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

" Let X be the unit Cartesian square ×, and let ~ be the equivalence relation on X defined by ∀ a, b ∈ (( a, 0 ) ~ ( a, 1 ) ∧ ( 0, b ) ~ ( 1, b )).

Let R be the quadratic mean ( or root mean square ).

Let be the columns of P, each multiplied by the ( real ) square root of the corresponding eigenvalue.

Let us now consider a three-dimensional cubical box that has a side length L ( see infinite square well ).

Let us consider a 2D solid, a set of atoms in a perfect square array,

* Let ; B is a 3x3 square, that is, B =

Let us consider a square array of classical spins which may only take two positions: + 1 and − 1, at a certain temperature, interacting through the Ising classical Hamiltonian:

Let n = 2, so that the array is 5x5 and the final square is 10x10.

Let be the unit square.

* Let E = Z < sup > 2 </ sup >; B is a 3x3 square, that is, B =

Theorem: Let V be a finite-dimensional vector space over a field F, and A a square matrix over F. Then V ( viewed as an F-module with the action of x given by A and extending by linearity ) satisfies the F-module isomorphism

Let A be a symmetric square matrix of order n with real entries.

Let z be the optical axis then one can deduce separately for the x and the y axis that the refractive power is again the square of the refractive power of a single lens.

Let A be a square matrix ( not necessarily positive or even real ).

" Oh, do not weep ", " Istanbul is such a fine red coral land ", " Zühre: In deep seas twine ", " I roam from land to land ", " Efe Song-Yörük Ali: Of all the cool and clear brooks ", " Sille square ", " Katurjolu zeybek ", " A zeybek blond and burly ", " I was born in Bergama ( Bergama 1 )", " Let me reach this cloudy mountain peak ", " I was born in Bergama ( Bergama 2 )", " In green meadows ".

Let be a square matrix, and for each denote by the matrix that results from by deleting the-th row and the-th column.

Let the value of the soldier's square be, then the total change in score after a positive jump is.

Let a be an integer which is not a perfect square and not − 1.

Banners hung in the square reading " Resistance is Fertile " ( a pun on futile ), " Let London Sprout ", " Capitalism is Pants ", and " The Earth is a Common Treasury for All ", the latter being a quote from the seventeenth-century Digger Gerrard Winstanley.

Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??