Let $$[a_1(x),a_2(x),a_3(x),\cdots ]$$ be the continued fraction expansion of $$x\in (0,1)$$ . This paper is concerned with certain sets fractions non-decreasing partial quotients. As a main result, we obtain Hausdorff dimension set $$\begin{aligned} \left\{ x\in (0,1): a_1(x)\le a_2(x)\le \cdots ,\ \limsup \limits _{n\rightarrow \infty }\frac{\log a_n(x)}{\psi (n)}=1\right\} \end{aligned}$$ fo...

laminar counterflow diffusion flames provide useful information about basic properties of non-premixed combustion. a lot of studies have been performed on h2/o2 counterflow. most of previous studies include undiluted or diluted systems of hydrogen (with co2 or n2) against an air flow under a variety of conditions such as strain rates, inlet temperature and pressure. the main purpose of this res...

We consider scheduling jobs online to minimize the objective ∑ i∈[n] wig(Ci− ri), where wi is the weight of job i, ri is its release time, Ci is its completion time and g is any non-decreasing convex function. Previously, it was known that the clairvoyant algorithm Highest-DensityFirst (HDF) is (2 + )-speed O(1)-competitive for this objective on a single machine for any fixed 0 < < 1 [21]. We s...

The reproductive performance of a dairy herd has a significant effect on the profitability of that herd. Common measures of reproductive performance are days to first service, days to conception, calving interval, services per conception, conception rate, estrus detection rate, and pregnancy rate. Most cow operations would benefit economically by reducing the number of operational days, decreas...