Sentence examples similar to gives begin from inspiring English sources

i) Condition F gives begin{aligned} sum _{iin mathbf {N}}T_{i}(psi )=Theta Gamma (Theta ).

end{aligned} (38 Combining (37) and (38) gives begin{aligned} -Theta Gamma _{j}(Theta )+ n-1 Gamma (Theta )=0.

end{aligned} (33) The exact form (2) gives begin{aligned} u = (T-t)^{-2/ 3p }psi z)+mbox{bounded term}.

This property gives: begin{array}rcl@ begin{aligned} begin{array}{ll} {s_{j}} geq 0 & forall j in boldsymbol{j}.

(17) Separating the real and imaginary parts gives begin{aligned} &-{omega}^{2}+b=dcosomega tau+comegasinomegatau, &aomega=comegacosomegatau-dsinomegatau.

end{aligned} Since (piinPi), Lemma 2.2 gives begin{aligned} lim_{ntoinfty}{omega_{lambda/a}(hx_{n+1},hx_{n})}=0.

end{aligned} Using the integration by parts equation gives begin{aligned} int_{0}^{infty}f(x), ^{R}_{x} !

By identifying matrices with corresponding linear operators, [35, Lemma 3.3] gives begin{aligned} {text {Op}}(a) = D_{phi _1}circ A circ C_{phi _2}.

For the no-tax economy, using Stein's Lemma gives: begin{aligned} mathbf {p}=frac{E[mathbf {X}]}{R_mathrm{f}}+-frac{alpha _i}{R_mathrm{f}}Omega mathbf {n}_{ri}.

end{aligned}Letting ( gamma longrightarrow 0) gives begin{aligned} sup _{xin H_{u}(t)} |x|ge chi (t) quad t>0.

Substituting (overline{s}) from (6) into (4) and (5) gives begin{aligned} E(Lmid overline{s})=E(Rmid overline{s})=frac{a-c}{1-c}overline{R}.