Sentence examples for minimal index from inspiring English sources

Among the many places in the pre-set of (t_j), the one with minimal index (as we assume that places are indexed) plays the role of leader of the multi-party synchronization (i.e., the process performing the atomic sequence of inputs (x^j_i) to be synchronized with single outputs (bar{x}^j_i) performed by the other servant participants).

But the book's principal shortcomingsare a severe case of erratic spelling, particularlyof proper nouns, a minimal index andlight blue captions that are hard to read.

Let u be the minimal index such that (x_0,ldotsdots,x_nin G_u).

Indeed, let N be a normal subgroup of G and let i be the minimal index such that (Ncap G_{i+1}ne 1).

end{aligned}Let now s be the minimal index for which (Ncap E_sne 1) and choose a nontrivial element (xin Ncap E_s).

The minimal index is shown to be multiplicative: if M1 ⊂ M2 ⊂ M3 are factors, then Ind(M1, M3) = Ind(M1, M2) Ind(M2, M3), extending a previous result (H. Kosaki and R. Longo, J. Funct. Anal.107 (1992), 458 470).

and row minimal indices (r.m.i). of s F − G respectively.

Proof First we consider that the system has non-zero column minimal indices and non-zero row minimal indices.

The set of minimal indices ϵ 1, ϵ 2, …, ϵ d and ζ 1, ζ 2, …, ζ t are known as column minimal indices (c.m.i).

∥ J p ∥ < 1 ; the column minimal indices are zero, i.e., dim N r ( s F − G ) = 0 ; (45).

It is clear that the existence of the column minimal indices is the reason that the systems (31) and consequently (33) exist.