Sentence examples for this paper suppose from inspiring English sources
The following theorem is the main result of this paper: Suppose that Assumption 3.1 is satisfied.
end{aligned} Throughout this paper, suppose that the following two assumptions hold.
In this paper, suppose the considered 3D hollow cylinder domain is regular, and the internal and external radii are denoted (r_{0}) and R, respectively.
In this paper, suppose that ((E,|cdot|)) is a Banach space partially ordered by a cone (Psubset E), that is, (xleq y ) if and only if (y-xin P).
In this paper, suppose that σ ( s ) = ( σ 1 ( s ), …, σ N ( s ) ) and f ( s ) satisfy the following assumptions: where the constants in (H1) and (H2) are all positive and satisfy.
We assume all the coefficients are continuous bounded nonnegative functions on R + = [ 0, + ∞ ). If f ( t ) is a continuous bounded function on R +, define f u = sup t ∈ R + f ( t ), f l = inf t ∈ R + f ( t ). Throughout this paper, suppose that a 2 l > 0, m i l > 0 ( i = 1, 2, 3 ), b i l > 0 ( i = 1, 2 ).
For simplicity's sake, this paper supposes A, B, D, and F to be 5 min.
This paper supposes that the time-variant system is discrete in time and space with given probabilities of transition between space states.
This paper supposes that each time a management operation takes place, hosts are classified to three different power states: power on, power suspended, and power off.
In this paper, supposing that the relay and the destination are equipped with K antennas, we propose a new transmission protocol which enables 2.K uplink and downlink transmissions to be accomplished within (K + 2) time slots.
For the clustering area this paper supposed to aid education, the tool was designed for clustering algorithms used easy and effective, cut down of the time that is making programme by the students so with the using of data sets that belongs to students, results of the clustering that was supported graphical items shown with the help of user interface and clustering must be so effective and easy.
