Sentence examples for mu such that from inspiring English sources

By (i), there exists (x(mu inPhi(mu)) such that biglVert x lambda_{0}, mu_{0} -x(mu) bigrVert leq h_{Phi} Vert mu-mu_{0} -xt ^{alpha}.

Then, by (i), there exists (x(mu inPhi(mu)) such that biglVert x lambda_{0}, mu_{0} -x(mu) bigrVert leq h_{Phi} Vert mu-mu_{0} -xt ^{alpha}.

For each (muin N(mu_{0})), we consider the following parametric equilibrium problem (PEP): Find (x in K(mu)) such that f (x, y, mu) geq0, quad forall y in K(mu).

Give a characterization of those measures (mu ) such that (S_mu in mathfrak I_c).

Then, for each (uin X) with (Muneq emptyset ), there exists (x_{0}in Mu) such that (Mx_{0}subset {x_{0}}).

There exists a constant (N = N(C_D) > 0), called homogeneous dimension of K with respect to ((Xi, d, mu )), such that (|B x,r)| le C_D tau ^{-N} |B x,tau r)|), for all (0 < tau le 1).

Namely we assume for any constant (a > a_0), there exist non-negative constants (mu _0) and (mu _1) such that begin{aligned} rcdot F_r le F + mu _0 + mu _1{mathscr {T}} end{aligned} (3.24 whenever (F ge a).

The fragment was trimmed with BamHI and ligated into a BamHI site of Cat-Mu such that the selectable marker genes (trp and cat) are transcribed in opposite directions.

Since T satisfies the condition ((E_mu )) on C, there exists (mu > 1) such that begin{aligned} d(x_n, Tx) le mu d(x_n, Tx_n) + d(x_n, x).

For the latter estimates we also need to assume in case (ii) a complementary condition to (3.24), namely that there exist non-negative constants (mu _0), (mu _1) and (mu _2) such that for any (rin Gamma ), begin{aligned} -rcdot F_r le mu _0 + mu _1 {mathscr {T}}(r) + mu _2 |F r)|.

(10) By (2), it is easy to check that there is some (M>2) such that mu bigl(B z,2r) bigr)leq Mmu bigl(B z,r) bigr).