Let D be a weighted oriented graph and I(D) be its edge ideal. In this paper, we show that all the symbolic and ordinary powers of I(D) coincide when D is a weighted oriented certain class of tree. Finally, we give necessary and sufficient conditions for the equality of ordinary and symbolic powers of naturally oriented lines.

Molecular identification/ characterization of Bemisia tabaci (Genn.) collected across five agroecological zones of West Bengal, India revealed that it resembles genetic group Q. Seed treatment with thiamethoxam 70WS 3 g/ kg seed incorporated with seedling treatment with acetamiprid 20SP @ 1g/ l, seedling rising under insect proof net and border netting with insect proof net showed efficacy with reducing the occurrence and dispersal of thrips Scirtothrips dorsalis Hood, mite Polyphagotersonemus latus and whiteflies B. tabaci; while their least incidence was observed with IPM module (integration of seed treatment, seedling treatment, seedling raising under insect proof net, border netting technology, installation of yellow sticky trap and need based spot application of spiromesifen and diafenthiuron), with 92.97, 82.68 and 72.97% reduction, respectively; and 98.56% reduction of chilli leaf curl virus (CLCV) incidence could be obtained through IPM with maximum yield of green chili (1.66 t/ ha). Panchagavya, dasaparni and bhramvastra appeared as potent biopesticides in reducing the CLCV causative agents.

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Let [Formula: see text] be a weighted oriented graph and [Formula: see text] denote the corresponding edge ideal. In this paper, we give a combinatorial characterization of [Formula: see text] which has a linear resolution. As a consequence, we prove that if [Formula: see text] is the edge ideal of a weighted oriented graph [Formula: see text], then [Formula: see text] has a linear resolution if and only if all powers of [Formula: see text] have a linear resolution. Also, we prove that if [Formula: see text] is a weighted oriented graph and [Formula: see text] for all [Formula: see text], then [Formula: see text] has a linear resolution if and only if all powers of [Formula: see text] have linear quotients. We provide a lower bound for the regularity of powers of edge ideals of weighted oriented graphs in terms of induced matching. Finally, we obtain a general upper bound for the regularity of edge ideals of weighted oriented graphs.

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