Abstract We show that there is a red-blue colouring of $[N]$ with no blue 3-term arithmetic progression and red length $e^{C(\log N)^{3/4}(\log \log N)^{1/4}}$ . Consequently, the two-colour van der Waerden number $w(3,k)$ bounded below by $k^{b(k)}$ , where $b(k) = c \big ( \frac {\log k}{\log k} )^{1/3}$ Previously it had been speculated, supported data, $w(3,k) O(k^2)$

   Stability of bacterial flora in fish intestine is very important, because the intestine is an important organ for outbreak of microbial infections and other fish diseases especially when the fish have not been vaccinated. The aim of this study was to determine the bacterial flora of intestine in sturgeon juvenile in earthen ponds. The results can be applied to prevent the diseases occurren...

In this study, random sampling conducted and 90 individuals of Persian sturgeon having 3-5g weight, collected by trawling in 3 earthen ponds and 15 individuals having 10-20g weight, collected by small net in 3 fiberglass Vans. After recording of biometrical characteristics, the intestine and rearing water were cultured on TSA medium. Gram staining and complementary tests were conducted. In orde...

In the fall and winter of 1965-1967, 292 ratfish (Hydrolagus colliei) Wi!re collected from four locations off the Pacific coast of Oregon. Specimens were examined for length-weight relationships, food habits, parasites, and a method of sex and age determination. Equations describing the body weight-body length (snout to vent) relationships were log weight = log -4.3217 + 3.0546 log length for m...

We study the problem of uniformly partitioning the edge set of a tree with n edges into k connected components, where k ≤ n. The objective is to minimize the ratio of the maximum to the minimum number of edges of the subgraphs in the partition. We show that, for any tree and k ≤ 4, there exists a k-split with ratio at most two. (Proofs for k = 3 and k = 4 are omitted here.) For general k, we pr...

Let D be a b-wise independent distribution over {0, 1}m. Let E be the “noise” distribution over {0, 1}m where the bits are independent and each bit is 1 with probability η/2. We study which tests f : {0, 1}m → [−1, 1] are ε-fooled by D + E, i.e., |E[f(D+E)]−E[f(U)]| ≤ ε where U is the uniform distribution. We show that D+E ε-fools product tests f : ({0, 1}n)k → [−1, 1] given by the product of k...

We present an implementation of split-population duration regression in the spduration (Beger et al., 2017) package for R that allows for time-varying covariates. The statistical model accounts for units that are immune to a certain outcome and are not part of the duration process the researcher is primarily interested in. We provide insights for when immune units exist, that can significantly ...

We study the problem how uniformly one can partition the edge set of a tree with n edges into k connected components, where k ≤ n. The objective is to minimize the ratio of the maximum to the minimum number of edges of the subgraphs in the partition. We show that, for any tree and k ≤ 4, there exists a k-split with ratio at most two. For general k, we propose a simple algorithm that finds a k-s...

The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the Johnson-Lindenstrauss property involve randomness. We address the question of explicitly constructing such embedding families and provide a construction with an almos...