Given a line arrangement A with n lines, we show that there exists a path of length n/3−O(n) in the dual graph of A formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we describe an example of a line arrangement with 3k blue and 2k red lines with no alternating path longer than 14k. Further, we show that any line arrangement with n lines has a coloring ...

The realizability problem for rank 3 oriented matroids (see [1]) is equivalent to the pseudoline stretchability problem (see [4]). This paper uses an example to illustrate a new approach to this problem. The main theorem of this paper, like the trigonometric form of Ceva’s theorem, shows a non-trivial relationship amongst the angles in a specific line arrangement figure (c). We work in polar co...

The present study was conducted to investigate the effect of dietary supplementation of turmeric (TEO) and rosemary (REO) essential oils on growth performance and oxidative stability of broiler meat. Five hundred forty day-old chickens (Cobb 500) were randomly allotted to a 3 × 3 factorial arrangement with three levels of turmeric essential oil (T1=0, T2=75 and T3=150 mg/kg) and three levels of...

This study was done to evaluate the effect of different planting arrangements (square, lozenge and rectangular) and various concentrations of potassium sulfate (K2SO4) fertilizer (0, 100, 200 and 300 kg/ha) on yield and essential oils quantitative of Calendula officinalis L., a medicinal and ornamental plant. The experiment was done as a factorial in randomized completely blocks design (R.C.B.D...

This experiment was aimed to evaluate the effect of amalgamated NPS chemical fertilizer on crop performance and nodulation soybean (Glycine max L (Merrill)) varieties acidic soil during 2020 cropping season. Varieties i.e “Katta” “Korme” six levels were used in factorial arrangement within randomized complete block design with three replications. Nodule parameters highly influenced (P<.001) ...

Non-regular two-level fractional factorial designs, such as Plackett–Burman designs, are becoming popular choices in many areas of scientific investigation due to their run size economy and flexibility. The run size of nonregular two-level factorial designs is a multiple of 4. They fill the gaps left by the regular twolevel fractional factorial designs whose run size is always a power of 2 (4, ...