ϕ ( t ) < t, lim r → t + ϕ ( r ) < t for each r > 0. Since we want to shorten expressions in the following theorem, consider Condition 1 in the following for X an F. Condition 1 Suppose either (i) F is continuous, or (ii) X has the following property: (a) if non-decreasing sequence x k → x, then x k ≤ x for all k, (b) if non-increasing sequence y k → y, then y k ≥ y for all k. .
As an example, IκBη and IκBζ were both shown to force IL-6 production in macrophages, as loss of these proteins shortened the expression period and the level of the secreted cytokines [ 64, 87].
Liquid and gaseous hydrocarbons are so intimately associated in nature that it has become customary to shorten the expression "petroleum and natural gas" to "petroleum" when referring to both.
A beaming smile and a cheeky twinkle in his eye accompany most of what comic says, but he's not without side, shortening the expression "charity muggers" into "chuggers" and then into something shorter and much ruder.
The arguments are dropped out to shorten the expression.
The biggest problems for computational processing are typing errors, various length of shorten expressions and usage of synonyms.
Our previous in vivo study demonstrated that human nucleus pulposus chondrocytes (NPCs) in aging discs exhibited characteristic senescent features such as an increased senescence-associated β-galactosidase (SA-β-gal) expression, shortened telomere, and decreased telomerase activity.
Consistent with these data, cycloheximide-chase assays revealed that the half-life of SREBP1c was shortened by ectopic expression of RNF20 (Fig. 3B).
In contrast to these results, lifespan was shortened by conditional expression of dilp6 with ubiquitous drivers, as well as when dilp6 was ubiquitously reduced by RNAi (Table 1; Figs S3 and S4).
For the group of patients who did not receive adjuvant chemotherapy, there were significant associations between PRAME expression levels and shortened overall survival (P<0.001), and PRAME expression levels and shortened metastasis-free interval (P<0.001).
