Sentence examples for 1 dots from inspiring English sources

quad forall n in { 1, dots, N }.

text{subject to:} R_{k} geq rho_{k}, quad forall k in { 1, dots, K }, (2).

A linear functional μ on (ell^{infty}) is called a mean if (mu e)=|mu|=1), where (e={1, 1, 1, dots }).

It should be noted that the processes (X^{1}, dots, X^{n}) and the associated remuneration processes (beta ^{1}, dots, beta ^{n}) do not represent traded assets.

Assume that ({eta_{nm}: m=1, dots, v}) are independent random variables, and the distribution of (eta_{nm}) is the same as that of (y_{nm}^{prime}) for (m=1, dots, v).

We assume that the numbers (p_{1},dots,p_{n},q_{j}) for (jinTheta_{1}^{a}) are distinct and that the numbers (p_{n+1}, dots,p_{2n},q_{j}) for (jinTheta_{1}^{b}) are distinct.

Let (Isubseteq mathbb {R}) be an interval and let (mathscr{M}colonbigcup_{n=1} ^{infty} I^{n} to I) be an arbitrary mean, i.e., for all (nin mathbb {N}) and ((x_{1},dots,x_{n})in I^{n}), we assume that (mathscr{M}) satisfies the inequality min(x_{1},dots,x_{n})leq mathscr{M}(x_{1}, dots,x_{n})leqmax(x_{1},dots,x_{n}).

The rigorous solution for ( {sigma}_{0i}^2left 1, dots, mright) ) can be delivered by solving the m dimensional equation system.

where we abbreviate, for example, (ln {boldsymbol pi } = left (ln pi _{1}, dots, ln pi _{n} right)).

Define the induced binomial point processes as (mathfrak {X}_{n} = left {X_{1}, dots, X_{n}right }).

The dashed boxes in Fig. 20 show the state machines for reconstructible sequences for (L_{text {scr}}=1, dots,4).