Sentence examples for progression of length from inspiring English sources

When I saw the problem I was intrigued because it was a new (to me) and natural variation of a bit of mathematics that I'd heard of before but hadn't thought that much about: one can bicolor {1,2,3,…,8} to avoid any monochromatic AP3 (arithmetic progression of length 3), but not {1,2,3,…,9}.

Van der Waerden's theorem states that if the positive integers are divided into any finite number of disjoint sets (i.e., sets without any members in common) and k is an arbitrary positive integer, then at least one of the sets contains an arithmetic progression of length k.

We scrutinized each step of amyloid progression of full length bovine carbonic anhydrase (BCA) and compared it with the amyloidogenic process of its critical peptide stretch 201 227 (PepB).

The effect of decreasing the progression of axial length was more pronounced in high myopia patients than in low myopia patients for both groups.

PROBLEM: Amyotrophic lateral sclerosis is a heterogeneous disorder with differing sites of onset, rates of progression, length of disease and pathological mechanisms.

The micro-motor which drives the zoom has a perceptible response-lag and drives the lens forward in 'chunks', rather than a seamless progression of focal-length.

Our idea was to systematically examine the same progression of DNA lengths that have been observed in vivo, but now using TPM experiments.

Statistical analysis showed that the following factors were linked to a higher risk of progression: length of symptoms before presentation and time taken to break the attack.

There are widespread (and correct) beliefs that the writing tasks that students are asked to undertake as they move through their undergraduate and graduate years show a broadly upward progression in terms of length, complexity of resources utilized, and sophistication expected.

Szemerédi proved the conjecture for four-term progressions in 1969 and for progressions of any length in 1975.

Later, they concede that the evidence is weaker or nonexistent that positive psychological states affect progression of cancer or length of survival time.