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 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 V, W and X be three vector spaces over the same base field F. A bilinear map is a function

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

Let F be a prefix-free universal computable function.

Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.

Let F be the continuous cumulative distribution function which is to be the null hypothesis.

Let F be a field.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

These assumptions can be summarised as: Let ( Ω, F, P ) be a measure space with P ( Ω )= 1.

Let the input power to a device be a force F < sub > A </ sub > acting on a point that moves with velocity v < sub > A </ sub > and the output power be a force F < sub > B </ sub > acts on a point that moves with velocity v < sub > B </ sub >.

Let P be the following property of partial functions F of one argument: P ( F ) means that F is defined for the argument ' 1 '.

Let F and G be a pair of adjoint functors with unit η and co-unit ε ( see the article on adjoint functors for the definitions ).

Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.

Let J and C be categories with J a small index category and let C < sup > J </ sup > be the corresponding functor category.

Let J be a directed poset ( considered as a small category by adding arrows i → j if and only if i ≤ j ) and let F: J < sup > op </ sup > → C be a diagram.

Let C be a category and let J be a small index category.

Let I be a finite category and J be a small filtered category.

Let F: J → C be a diagram.

J. Todd Moye, author of Let the People Decide: Black Freedom and White Resistance Movements in Sunflower County, Mississippi, 1945-1986, said " Sunflower County has always been overwhelmingly rural " and that, at the end of the 20th century, the county had four " main towns of any size.

Todd J. Moye, author of Let the People Decide: Black Freedom and White Resistance Movements in Sunflower County, Mississippi, 1945-1986, said that the white residents of Drew " traditionally been regarded as the most recalcitrant in the count on racial matters.

* " Don't Let Your Love Go Wrong " w. George Whiting & Nat Schwartz m. J. C. Johnson

* " Let The Rest Of The World Go By " w. J. Keirn Brennan m. Ernest R. Ball

* " Please Go ' Way And Let Me Sleep " w. Cecil Mack m. J. Tim Brymn

Let me borrow that ," referring to the microphone tattoo on LL Cool J's arm which LL Cool J accused Canibus of insulting him, went hard on him, and when the final cut of the song came out it featured LL Cool J's verse after Canibus, mocking an unspecified person believed to be Canibus.

Let J be the symplectic mapping

Let E and F be two vector bundles over a differentiable manifold M. An R-linear mapping of sections is said to be a kth-order linear differential operator if it factors through the jet bundle J < sup > k </ sup >( E ).

One category on the Revlon Category Board was " Jazz ", and within months of the premiere Columbia Records issued a 1955 album of various jazz artists under the tie-in title $ 64, 000 Jazz ( CL 777, also EP B-777 ), with the following tracks: " The Shrike " ( Pete Rugolo ), " Perdido " ( J. J. Johnson, Kai Winding ), " Laura " ( Erroll Garner ), " Honeysuckle Rose " ( Benny Goodman ), " Tawny " ( Woody Herman ), " One O ' Clock Jump " ( Harry James ), " How Hi the Fi " ( Buck Clayton ), " I'm Comin ', Virginia " ( Eddie Condon ), " A Fine Romance " ( Dave Brubeck, Paul Desmond ), " I Let A Song Go Out Of My Heart " ( Duke Ellington ) and " Ain't Misbehavin '" ( Louis Armstrong ).

In addition to rap, legendary smooth jazz musician Grover Washington, Jr., a fan of the 76ers, created the song " Let It Flow ( For Dr. J )", from the album Winelight, in honor of Erving.

Among these were " Let It All Hang Out " ( a cover of the 1967 track by The Hombres ), " It Only Takes A Minute " ( a cover of Tavares ' track ) as One Hundred Ton And A Feather, " Sugar, Sugar " as Sakkarin, " Loop di Love " as Shag, " Hooked on a Feeling " ( a cover of the track by B J Thomas ), " Lazybones ", " It's The Same Old Song " ( originally by Four Tops ) as The Weathermen and " The Sun Has Got His Hat On " as Nemo.

Let us first calculate exp ( J ).

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

: Theorem on projections: Let the function f: X → B be such that a ~ b → f ( a )

Let ( A < sub > i </ sub >)< sub > i ∈ I </ sub > be a family of groups and suppose we have a family of homomorphisms f < sub > ij </ sub >: A < sub > j </ sub > → A < sub > i </ sub > for all i ≤ j ( note the order ) with the following properties:

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Let V and W be vector spaces over the same field K. A function f: V → W is said to be a linear map if for any two vectors x and y in V and any scalar α in K, the following two conditions are satisfied:

Let M and N be ( left or right ) modules over the same ring, and let f: M → N be a module homomorphism.

Let F be a diagram that picks out three objects X, Y, and Z in C, where the only non-identity morphisms are f: X → Z and g: Y → Z.

Let G and H be groups, and let φ: G → H be a homomorphism.

Let T: X → X be a contraction mapping on X, i. e.: there is a nonnegative real number q < 1 such that

Let ( M, g ) be a Riemannian manifold and ƒ: M < sup > m </ sup > → R < sup > n </ sup > a short C < sup >∞</ sup >- embedding ( or immersion ) into Euclidean space R < sup > n </ sup >, where n ≥ m + 1.

Let U be an open subset of R < sup > n </ sup > and f: U → R a function.

Let U, V, and W be vector spaces over the same field with given bases, S: V → W and T: U → V be linear transformations and ST: U → W be their composition.

Let x < sub > t </ sub > be a curve in a Riemannian manifold M. Denote by τ < sub > x < sub > t </ sub ></ sub >: T < sub > x < sub > 0 </ sub ></ sub > M → T < sub > x < sub > t </ sub ></ sub > M the parallel transport map along x < sub > t </ sub >.

Let f: < sup > n </ sup > → be the fitness or cost function which must be minimized.

Let f: D → R be a function defined on a subset D of the real line R. Let I = b be a closed interval contained in D, and let P =