Sentence examples for we additionally suppose from inspiring English sources
From now on we additionally suppose that (X) is paracompact.
In order to prove our main results, we additionally suppose the following assumptions: (2.1).
Remark 2.3 If, in the above remark, we additionally suppose that x ∗, y ∗ ∈ Fix ( T ) ⇒ ( x ∗, y ∗ ) ∈ E ( G ), then Fix ( T ) = S Fix ( T ) = { x ∗ }.
If we additionally suppose that f is a harmonic mapping, then there exists a holomorphic function (g:mathbb {H}to mathbb {C}) such that (f z)= operatorname {Re}g z) +icy).
For the metric ({d_{L^p}}) (concerning distances between density functions at the same time instant later on), for example, we additionally suppose every test function (varphi in C^1_c({{mathbb R}^{N}})) to be in the unit ball of (W^{1, infty }({{mathbb R}^{N}})), i.e., (varphi ) is bounded and 1-Lipschitz continuous in addition.
We additionally suppose that this automaton is non d-ambiguous (a DFA having this property is also called a d-th order DFA in [ 48]), which means that for all q ∈, the set of sequences of length d that can lead to q is either a singleton or the empty set.
Additionally suppose that x and y are decreasing and satisfy conditions (1.7), (1.8).
Additionally suppose that (minmathbb{N}), (x_{i},y_{i}in [ a,b ] ) and (w_{i}inmathbb{R}) for (iin{1,2,ldots,m}).
Additionally suppose that (mathbf{x}, mathbf{y}in[ a,b]^{m}) are two decreasing m-tuples and (mathbf{w}inmathbb{R}^{m}) which satisfy conditions (1.4), (1.5).
In problem (1 - 3) let us additionally suppose that the function (Phi ( x ) ) is continuously differentiable and (f ( x,u,t ) ) is a continuously differentiable vector function with respect to x and u.
Additionally, suppose that [Z k,U k ] are acquired incrementally such that algorithm 1 is applied as new observations arrive such that ([Z_{k}^{s},U_{k}^{s}]) are vectors that belong to a particular segment s, i.e., they are produced due to an unique attractor.
