A series of Zariski pairs and four Zariski triplets were found by using lattice theory of K3 surfaces. There is a Zariski triplet of which one member is a deformation of another.

We have studied inflationary paradigm through an equation of state. With a single parameter state as function the scalar field responsible for accelerated expansion, we find observationally viable model satisfying all constraints laid down by recent observations. The resulting can efficiently cover wide range tensor-to-scalar ratio ranging from $r\sim\mathcal{O}(10^{-1})$ to $\mathcal{O}(10^{-6...

A variational treatment for a two-electron quantum dot (the artificial helium atom) is proposed which leads to exact answer for the ground state energy. Depending on the magnetic field value the singlet-triplet and triplet-triplet transitions of the ground state take place, which are captured in our solution.Using the same variational technique we find corrections to wave function and energy an...