Sentence examples for bounds in the case from inspiring English sources

Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes.

This means that it exceeded the bounds in the case of n=32 and n=64.

Beta distributions are estimated for prices and quantities of inputs and outputs based on the user-supplied mean and coefficient of variation for each variable, together with the minimum and maximum values involved (i.e. the bounds) in the case of prices.

The dependence on n is analyzed in Section 3. The use of the three-term recurrence relation allows us to obtain sequences of upper and lower bounds in the case d n (x e n (x) > 0; Turán-type inequalities are also established, as well as bounds on the logarithmic derivatives.

Due to the potential variable mutation effects and epistatic effects (1, 2), the genomic mutation parameters estimated here are lower bounds in the case of,, and upper bounds in the case of and.

It does not decrease the upper bounds in the case of a general HMM but leads to a significant improvement of the software for Markov models.

He was able to prove that (||u(t)||_2) (which is bounded in the case (-Delta +V) is bounded below) doesn't grow worse than (|t|^3) and then push through a variant of the Chernoff Nelson argument (since a (|t|^3) bound can eliminate exponential growth).

{ g y n } is bounded in the case ( f, S ) satisfies the (E.A -property, { f y n } is boundE.A -propertye ( g, T ) satisfies (E.A)-property.

{ g y n } is bounded in the case ( f, S ) satisfies the (E.A -property, or.

This, together with ((H_{7})), means that (Omega_{1}) is bounded in the case (p>2) and, similarly, for (1 < p leq2).

Therefore (H x,y)) is also bounded in the case (2) since (x^{alpha- lambda+1)}leq1) for (x^{alpha- lambda+1