Sentence examples for e equipped from inspiring English sources

A linear space E equipped with a countable system of compatible norms (|cdot|_{n}) is said to be countably normed.

(S(R^{n};mathbb{C})) is denoted by just S. Let (S^{prime }(R^{n} E)) denote the space of all continuous linear operators, (L Srightarrow E), equipped with the bounded convergence topology.

The functor (Psi ) sends (e in mathcal {E}) to (lambda (e)) equipped with the map (lambda (a):lambda (e) rightarrow Phi (lambda (e)) = lambda (Phi _dagger (e))), where (a:e rightarrow Phi _dagger (e)) is the adjunction map.

The symbol e designates the identity element of G. Let G be the Lie algebra of the Lie group G which is the tangent space T e G of G at e, equipped with Lie bracket : G × G → G.

S ( R n ; C ) denoted by just S. Let S ′ ( R n ; E ) denote the space of all continuous linear operators L : S → E, equipped with the bounded convergence topology.

Here, (C ( [ 0,T ],E ) ) stands for the Banach space of all abstract continuous functions (varphi(t)) defined on ([ 0,T ] ) with values in E equipped with the norm Vert varphi Vert _{C ( [ 0,T ],E ) }=max_{0leq tleq T} biglVert varphi(t) bigrVert _{E}.

We employ the notation (mathcal {L}_b(E,F)) for the space (mathcal {L}(E,F)) equipped with the topology of bounded convergence and, similarly, (mathcal {L}_p(E,F)) and (mathcal {L}_{sigma }(E,F)) stand for (mathcal {L}(E,F)) equipped with the topologies of precompact and simple convergence, respectively.

Let (E=C[0,1],Vert uVert =max_{tin[0,1]} vert u(t)vert ), the product space (Etimes E) be equipped with norm (Vert (u, v Vert =Vert uVert +Vert vVert ) for ((u,v in Etimes E), and P= Bigl{ uin E u(t geq0,tin[0,1], min_{tin J_{theta}}u(t geq gamma Vert uVert Bigr}.

After embedding, sections of 60 nm each were cut using a Leica Ultracut E ultramicrotome equipped with a 2 mm diamond knife.

Semi-thin (300 nm) sections were cut on a Reichert-Jung Ultracut E microtome equipped with a diamond knife and mounted onto silane-coated microscope slides for light microscopy.

Class E was equipped with disc brakes, while the Class B was equipped with drum brakes.