Sentence examples for let left from inspiring English sources

Let (left{ u_{n}right}) be a subsequence of (left{ x_{n}right}) with (A left{ u_{n}right} )=left{ uright}) and let (A left{ x_{n}right} )=left{ xright}.) Since (uin omega _{W}(x_{n})subseteq F(T),) fsrom (9) (lim nolimits _{nrightarrow infty }dleft( x_{n},uright)) exists.

A5 (downlink channel state information) Let (left {g_{1}^{(t)}right }) and (left {g_{2}^{(t)}right }) be two independent and i.i.d.i.d

Let (left{ x_{n}right} _{n=1}^{N}) be the observed data and (left{ z_{n}right} _{n=1}^{N}) the latent variables; the log likelihood function is given as follows: begin{aligned} lleft( theta right) =sum _{n=1}^{N}log,pleft( x_{n}mid theta right) =sum _{n=1}^{N}log left[ sum _{z_{n}}pleft( x_{n},z_{n}mid theta right) right].

Let (left{ a right} subseteq A) be the set of available data and (left{ m right} subseteq A) be the set of missing samples.

Let (left| cdot right| _{p}) be the normalized (p -adic absolute value with (left| p -adic _{p}=frabsolute) and let (q) be an indeterminate in (mathbb {C}_{p}) with (left| 1-qright| _{p}

To obtain the two-kink solutions, let left.

Let (left( X,dright) ) be a metric space.

Let (left( X,Gright) ) be a generalized (b -metric space.

Let (left{ x_{n}right} ) be defined by (1.6).

… The Angels are likely to let left-hander David Huff sign with a Korean professional team.

Let ({left| Y_ell ^mrightrangle } = Y) denote a spherical harmonic basis.