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Production and Advanced Spectroscopic Characterization of Solvothermal Liquefaction Products of Polystyrene,

Mahmoud Negm1, Eemeli Eronen1, Tarja Parkkinen1

  • 1Department of Chemistry and Sustainable Technology, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland.

Energy & Fuels : an American Chemical Society Journal
|February 4, 2026
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The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
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The total amount of energy acquired by primary producers in an ecosystem is called gross primary production (GPP). However, of this energy, producers use some for metabolic processes, and some is lost as heat, decreasing the amount of energy available to the next trophic level. The remaining usable amount of energy is called the net primary productivity (NPP). In terrestrial ecosystems, NPP is driven by climate, while light penetration and nutrient availability drive NPP in aquatic ecosystems.
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Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...
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The dot product is an essential concept in mathematics and physics.
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