Sentence examples for under these assertions from inspiring English sources

Under these assertions, the functionals T ( n ) : = K n + T n ( r, s ) (103).

We require also additionally a m b m + 1 > 0 and a 0 b 0 > 0. (1) Under these assertions, there exists to every pair of nonnegative real numbers with ρ 2 + σ 2 > 0 precisely one solution f : Ω ( r, s ) → R + to (91) where the pair of positive numbers ( r, s ) is assumed as fixed.

Under these assertions, the following statements hold: (1) The evaluation of all elements P m ( m ∈ N 0 ) of the tripolynomial function system at two adjacent nodes z 1 and z 2 of the particular polynomial P j yields complete information on a sequence of new polynomials T n ( n ∈ N 0 ).

Not only are these assertions insensitive to the immense suffering of Palestinians under brutal military occupation and siege, but they are also detached from reality.

I accepted these assertions".

These assertions are not new.

Both these assertions are wrong.

Pakistani officials deny these assertions.

These assertions are basically true.

Mr. Montalvan has denied these assertions.

Is there some truth to these assertions?