We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, any surface X and an ample line bundle A on X, we have K + t base point free ≥ 3 very 4 .

Let X be a smooth projective curve of genus g ≥ 2 defined over an arbitrary algebraically closed field K. For any vector bundle E on X, call μ(E) := deg(E)/rank(E) the slope of E. A vector bundle E on X is said to be spanned if the natural map H(X,E)⊗OX → E is surjective. Such bundles are important tools for the projective geometry ofX because they are exactly the vector bundles associated to a...

Bubble columns are gas- liquid contactors that are widely used in chemical and bio- chemical industries. High mixing that result in high heat and mass transfer rates are amongst their advantages. Heat transfer in a bubble column having a bundle of heaters investigated and the variation of heat transfer coefficient with variation in heaters pitch to diameter ratios in a bundle of heaters reporte...

We prove the bigness of Chow–Mumford line bundle associated to a Q \mathbb {Q} </mml:semantic...