Sentence examples for defining a sequence from inspiring English sources

It is based on defining a sequence of functions { ϕ k } k = 0 ∞ and showing that ϕ k will successively approximate the solution ϕ in the sense that the 'error' between the two monotonically decreases as k increases.

Defining a sequence of stopping times: begin{aligned}& tau_{1}=infbigl{ tgeq0: x t geq theta_{2}bigr},& tau_{2k}=infbigl{ tgeqsigma_{2k-1}: x(t)leq theta_{1} bigr}, qquadtau_{2k+1}=infbigl{ tgeq sigma_{2k}: x(t)geqtheta_{2} bigr},quad k=1,2,ldots.

In order to prove that the velocity u ( t ) (representing the solution of the Euler equations (1)) stays (locally) in the function space B 1, 1 d + 1 ( R d ), we start with defining a sequence { u m } m ∈ N of vector fields depending on time by means of the following restrictions on each initial vector field: u m | t = 0 = S m u 0, m = 1, 2, 3, …, ∂ ∂ t u m + ( u m, ∇ ) u m = − ∇ p m. (2).

The 200 bp threshold used to define these elements is arbitrary and we therefore sought to determine empirically what the appropriate threshold length should be for defining a sequence as ultraconserved.

The IntelLEO Workflow ontology defines concepts such as roles and users, and allows defining a sequence of activities and tasks.

To overcome this problem de los Campos et al. (2010) proposed using a multikernel approach (named kernel averaging, KA) consisting of: (a) defining a sequence of kernels based on a set of values of h, and (b) fitting a multikernel model with as many random effects as kernels in the sequence.

Define a sequence such that.

To this end, define a sequence by.

Define a sequence such that (3.17).

and define a sequence in by (1.12).

Define a sequence such that, where,  .