In this paper, we consider the existence of a ground state nodal solution and solution, energy doubling property asymptotic behavior solutions following fractional critical problem \begin{document}$ \begin{equation*} \begin{cases} (a+ b\int_{\mathbb{R}^{3}}(|(-\Delta)^{\alpha/2}u|^{2})dx)(-\Delta)^{\alpha}u+V(x)u+K(x)\phi u = |u|^{2^{\ast}-2}u+ \kappa f(x,u), (-\Delta)^{\beta}\phi K(x)u^{2}, \q...

Lowest energy spectrum of the $^{12}$C nucleus is analyzed in 3$\alpha$ cluster model with a deep $\alpha\alpha$-potential Buck, Friedrich and Wheatley Pauli forbidden states $S$ $D$ waves. The direct orthogonalization method applied for elimination 3$\alpha$-Pauli states. effects possible first order quantum phase transition are shown lowest $^{12}$C($0_1^+)$ $^{12}$C($2_1^+)$ from weakly boun...

We describe our experience porting the Regensburg implementation of the DD-αAMG solver from QPACE 2 to QPACE 3. We first review how the code was ported from the first generation Intel Xeon Phi processor (Knights Corner) to its successor (Knights Landing). We then describe the modifications in the communication library necessitated by the switch from InfiniBand to Omni-Path. Finally, we present ...

A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a $K^{\alpha}$-translator of the flow by powers Gauss curvature if satisfies $K^{\alpha} = \langle N, \vec{v} \rangle$, $\alpha \neq 0$, where $K$ curvature, $N$ unit normal vector field and $\vec{v}$ direction $\mathbb{R}_1^3$. In this paper, we classify all rotational $K^{\alpha}$-translators. This classification will depend on...