Sentence examples for continuous joining from inspiring English sources

Laser technology is a good alternative for continuous joining of thermoplastics composites structures.

Now recall that the vector λ, which is involved in all the above-stated relations, is the 'gluing' parameter determining the pair of auxiliary boundary value problems (4.1), (4.2) and (4.3), (4.4), for which a continuous join described by Proposition 4.3 is possible.

We have constructed a continuous path joining and.

Next, we introduce the path given by for all which is obviously continuous in joining and.

In the end, we combine the curves, and to obtain a continuous path joining and.

Γ denotes the class of continuous paths joining 0 to u 1 in X, X ∗ denotes the dual space of X.

So g 1 is a continuous function joining the points ( 0, 0 ) and ( a 1, 1 ), and g 1 ( 1 ) ∈ ( g 1 ( a 2 ), 1 ).

Let (cgeqbeta) be characterized by c=inf_{gammainGamma}max_{sin[0,1]}Ibigl(gamma(s bigr), quad textit{where } Gamma=bigl{ gammain Cbigl([0,1],Ebigr);gamma(0)=0, gamma(1)=u_{1}bigr} is the set of continuous paths joining 0 and (u_{1}).

Let (cgeqbeta) be characterized by c=inf_{gammainGamma}max_{0leq tleq1}Ibigammamma(t) bigr), where (Gamma={gammain C [0,1],E), gamma(0)=0, gamma(1)=u_{1}}) is the set of continuous paths joining 0 and  (u_{1}).

Suppose E is a real Banach space, J ∈ C 1 ( E, R ) satisfies the following geometrical conditions: (i) J ( 0 ) = 0 ; there exists ρ > 0 such that J | ∂ B ρ ( 0 ) ≥ r > 0 ;   (ii) There exists e ∈ E ∖ B ρ ( 0 ) ¯ such that J ( e ) ≤ 0. Let Γ 1 be the set of all continuous paths joining 0 and e: Γ 1 = { h ∈ C ( [ 0, 1 ], E ) | h ( 0 ) = 0, h ( 1 ) = e },  .

The discretization error of is characterized by its worst-case upper (resp. lower) error which, because E β [ U] is monotone in β, is given by the area between the piecewise continuous function joining the measured values of E β [ U] and the upper (resp. lower) step function built from them [ 18].