Sentence examples for next result in from inspiring English sources

The next result in [9] is stated for order-preserving maps on (mathbb{R}^{n}) and it also holds in ordered Banach spaces [10].

Now we state our next result in: Theorem 4. Let f: Δ ⊆ ℝ2 → ℝ be a partial differentiable mapping on Δ: = [a, b] × [c, d] with a < b, c < d.

The discovery that the number of chromosomes remains constant from one generation to the next resulted in the full description of the process of meiosis.

"They then have to borrow again, and that is what leads to the cycle of rolling over loans from one month to the next, resulting in huge interest charges".

His plunge in public popularity can be traced to his fumbling of the state budget--too quick to tax one year, too unyielding the next, resulting in summer gridlock and embarrassing IOUs.

The nucleotides are joined to one another in a chain by covalent bonds between the sugar of one nucleotide and the phosphate of the next, resulting in an alternating sugar-phosphate backbone.

By comparison, when disease risk is small, vaccine coverage is highly variable from one cohort to the next, resulting in irregular patterns and more frequent outbreaks (Figure 1).

So at low to moderate stimulus frequencies, we see unfused tetani showing a treppe pattern in which the force builds from one stimulus to the next, resulting in greater maximum force with low frequency stimulation.

The proof of the next result is in [20].

The next result appears in Chapter 3, Theorem 9 of [15].

The next result proved in [11] concerns the convergence of sequences of functions correlated to solutions of the previous equation.