Given a graph G $G$ , decomposition of is partition its edges. A ( d h ) $(d,h)$ -decomposable if edge set can be partitioned into $d$ -degenerate and with maximum degree at most $h$ . For ≤ 4 $d\le 4$ we are interested in the minimum integer ${h}_{d}$ such that every planar $(d,{h}_{d})$ -decomposable. It was known 3 ${h}_{3}\le 2 8 ${h}_{2}\le 8$ 1 = ∞ ${h}_{1}=\infty $ This paper proves ${h}...

An convenient one-pot approach for the synthesis of new (E)-2-(2-oxo-4-phenylbut-3-en-1-yl)benzo[d]thiazole-3(2H)-carboxylates is demonstrated. The method based on a three-component reaction benzylideneacetone with electrophilic N-alkoxycarbonylbenzothiazolium species formed in situ. newly synthesized compounds were fully characterized by 1D 1H, 13C- NMR, IR and MS.

ABSTRACT- Despite the benefits of herbicides, their persistence in soil can harm other plants in next rotations and contaminate ground water. The main purpose of this research is to simulate 2,4-dichlorophenoxyaceticacid(2,4-D) movement in silty clay loam soil using HYDRUS-1D model in a corn root zone. The maximum contaminant level goal, MCLG, of 2,4-D in water resources is 10 ppb. The 3.5 kg a...