We define and study a family of cubic surfaces in the projectivized tangent bundle over a four dimensional projective space associated to the root system D 5. The 27 lines are rational over the base and we determine the classifying map to the moduli space of marked cubic surfaces. This map has degree two and we use it to get short proofs for some results on the Chow group of the moduli space of...

Stearic acid (SA) is highly soluble in structurally diverse solvents. SA/solvent packing within a (24.8 A)3 cubic volume explains the stoichiometry of SA solubility at multiple temperatures in multiple solvents. In the absence of solvent, the cubic volume contains 25 molecules at van der Waals distances from each other. At 55 degrees C, SA occupied half the cubic volume in saturated solution of...

Let $K$ be a number field, and let $E/K$ an elliptic curve over $K$. The Mordell--Weil theorem asserts that the $K$-rational points $E(K)$ of $E$ form finitely generated abelian group. In this work, we complete classification finite groups which appear as torsion subgroup for cubic field. To do so, determine on modular curves $X_1(N)$ \[N = 21, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 45, 65...

in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

Molybdenum is a refractory metal that is stable in a body-centred cubic structure at all temperatures before melting. Plastic deformation via structural transitions has never been reported for pure molybdenum, while transformation coupled with plasticity is well known for many alloys and ceramics. Here we demonstrate a structural transformation accompanied by shear deformation from an original ...