Sentence examples for begin with assuming from inspiring English sources
Although a Caledonian state could more or less pay its way to begin with, assuming that it was able to hold on to most of the North Sea oil- and gas-fields, that resource is drying up.
Throughout this section, we begin with assuming that N n, n = 1, 2, … , are positive integer-valued random variables independent of all X n k, k = 1, 2, …, n ; n = 1, 2, … , which are supposed to obey the relation N n → P + ∞ as n → + ∞. (10).
Given Equation (4), we begin with assuming that d l = c l, i.e., a conventional matched filter receiver is used, and consider minimization of the denominator in (4), which is equivalent to optimizing γ l since | | c l | | = 1 ( | | · | | denotes the Euclidean norm of a complex vector).
To begin with, assume that ΔR and ΔD are sufficiently small so that Q ˜ ( X ) is invertible.
To begin with, assume the first CN shall be placed, the GDOP of the TOA-based cooperative system is found to be G D O{P}_{mathrm{C}hbox mathrm{TOA}}^1=sqrt{frac{N+1}{{disin}^2left {beta}_1-{alpha}_nright({beta}_1-{alpha}_nright)}+{displaystyle sum_{n=1}^{N-1}{displaystyle sum_{m= n+1}^N{ sin}^2left({alpha}_n-{alpha}_mright)}}}} (20).
The volume-constrained improvement of the designs for heat flow begins with assuming the simplest structure, where a single line serves as heat source.
To begin with, it assumes an easy distinction between how and what that rarely exists in practice.
To begin with, we assume that the sequence { x k } generated by Algorithm 2 has a unique limit point x ∗.
To begin with, we assume that the initial function satisfies begin{aligned} vert nabla w_{0} vert le vert nabla u_{0} vert ^{p-1}.
To begin with, we assume that the reader is familiar with the basic results and the standard notations of the Nevanlinna theory of meromorphic functions (see [1 3]).
To begin with, we assume in the present article that the pressure-density functions satisfy P 1 ( n ) = P 2 ( n ) = n γ, γ ≥ 1, and set τ1, τ2 and λ to be one for simplicity In particular, we note that γ = 1 is an important case in the applications of engineer.
