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In this paper, we employ several class of transforms like binomial, k-binomial and rising transforms to the k-Lucas sequence. Moreover, we investigate some interesting properties between the so-obtained new sequences and the k-Lucas sequence.

Pesticide leaching and soil contamination are major issues in the present agriculture formulations. Hence, here 2D graphene oxide in combination with cationic, anionic, or nonionic polymers were tested for runoff resistance and targeted release behavior. Cationic polymer supplemented the binding of rGO on leaf surface by 30% more than control and reduced off-target leaching in soil by 45% more than control. Further, to enhance the fruit rot control caused by Colletotrichum capsici in chili crop, the rGO was decorated with Cu2–x Se nanocrystals, which provided combined disease control with captan. The chitosan coating in the nanocomposite added targeted pH-responsive fungal inhibition behavior and could reduce the C. capsici growth by ∼1/2 times compared to captan control.

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