In this study we have obtained some sufficient conditions for the Taketa inequality namely $dl(G)\leq |cd(G)|$ for finite solvable groups $G$.

Let $\mathcal{A}$ be a BSE Banach algebra and $\mathcal{B}$ be an essential abstract Segal algebra with respect to $\mathcal{A}$. In this paper we present a necessary and sufficient condition for $\mathcal{B}$ to be a BSE algebra as well. Furthermore we study BSE property of some certain abstract Segal algebras which are not discussed in previous works.

In this paper we define affine translation surface and classify minimal affine translation surfaces in three dimensional Euclidean space.

We show the equivalence of several definitions of compact infra-solvmanifolds that appear in various math literatures.

In this paper, we compute Alexander polynomials of the dual curves of certain smooth quartic curves. From our previous paper, all of these dual curves are $(2,3)$ torus curves of degree 12. As a consequence, from these curves, we find a new Zariski pair $12E_{6}+16A_{1}$, with different Alexander polynomials.

For an elliptic curve $E: y^{2} = 4(x^{3} + A x +B)$ over a field of characteristic $\neq 2$, we explicitly compute the pullback to the formal completion of $E$ at the origin of some important objects on $E$ including the functions $x$, $y$ and the invariant differential $\omega=dx/y$ in terms of the formal parameter $t = -2x/y$.