In a trilogy of cases, the Supreme Court applied the Eighth Amendment to the entire category of juvenile offenders, repudiated its “death is different” jurisprudence, and required states to consider youthfulness as a mitigating factor in sentencing. Roper v. Simmons prohibited states from executing offenders for murder they committed when younger than eighteen years of age. Roper reasoned that ...

Abstract Much of the Martian surface is covered by a weathering layer (regolith or soil) produced long-term processes such as impact gardening, eolian erosion, water weathering, and glacial modifications. China’s first mission, Tianwen-1, employed Mars Rover Penetrating Radar (RoPeR) to unveil detailed structure regolith assess its loss tangent. The RoPeR radargram revealed local be highly hete...

let $f$ be a locally univalent function on the unit disk $u$. we consider the normalized extensions of $f$ to the euclidean unit ball $b^nsubseteqmathbb{c}^n$ given by$$phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in b^n$ and$$psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$in which $betain[0,1]$, $f(z_1)neq 0$ and $...

We consider an effective field theory of unstable particles (resonances) using the complex-mass renormalization. As an application we calculate the masses and the widths of the ρ meson and the Roper resonance.