Sentence examples for subsequent notation from inspiring English sources

To simplify the subsequent notation define the matrix function by Now, taking into account (3.6), define the nonnegative real functional by (3.7).

The subsequent notation, for, stands for switching points of the rule acting on the primary class of self-maps from to being within the subset If the arguments and are omitted, then is understood to be within any subset of.

In the context of genomics, y is the phenotype, A is a matrix of genotypes (in subsequent notation we will refer to it as g), x a vector of effect sizes, and the noise is due to nonlinear gene-gene interactions and the effect of the environment.

In the following, we will focus without loss of generality on a single OFDMA subchannel, thereby omitting subchannel index ℓ in all subsequent notations.

The subsequent table (notation adjusted) is taken from Wansing 2006 and lists several pairs of conditions that may each be regarded as syntactic characterizations of notions of contradictoriness.

For simplicity, we will adopt in the subsequent sections the following notations: S = fft s (9).

In [14], the parameter α can take any value of the interval ([0.8,1)). Obviously, the parameter α in this paper can also obtain the lower bound 0.8 if (gamma=1). Let us introduce some matrices to simplify our notation in the subsequent analysis.

To illustrate our notation and lay grounds for subsequent formalism involving conformational dynamics of the enzyme, we begin with presenting a classical mass-action framework used to obtain rate-law for an arbitrary reaction scheme.

To simplify the notations, we drop in all subsequent equations the OFDM symbol index m from all matrices and vectors used in Equation (1).

Subsequent ballet masters turned to a form of notation using stick figures, the first of which was La Sténochorégraphie ("The Art of Writing Dance"), published in 1852 by the French dancer and choreographer Arthur SArthuréon.

This section also sets out the notation, algorithms, and structures required for subsequent sections.