Sentence examples similar to ling I from inspiring English sources

It can easily be proved that the condition of the theorem leads to (beta I le (I - sum_{i = 1}^{m} A_{i}^A_{i} )^{frac{1}{r}}).

Then (mathop{min} _{1 le i le n} r_{i} lerho(A) lemathop{max} _{1 le i le n} r_{i}).

Then for any (1 le i le j le ), (M_{j} subset M_i).

S i : the ith sensor, (1 le i le N, S_{i} in mathcal {N}).

For each (1 le i le m), let (C_i=C_{i,1} sqcap cdots sqcap C_{i,n}).

Assume that each color (c_i) is associated with cost 1, where (1 le i le g).

(eta _{1 le i le 4}) are negative and (eta _5) is positive, as expected.

All (sigma _i) for all clusters (C_i) ((1 le i le K)) follow Pareto distribution ((alpha)).

Then the elements (x_iGamma _2), (1 le i le m), generate the Lie ring (L(Gamma )).

(Vert {{e^{tA}}} Vert le M{e^{ - gamma t}} ) for some constant M and (gamma> 0 ); (sup _{1 le i le N} vert {{alpha _{i}}} vert < infty), (sup _{1 le i le N} vert {{beta_{i}}} vert < infty).

The time series Y is sampled in time steps t(i), (1 le i le n).