Correcting Mandatory Injustice: Judicial Recommendation of Executive Clemency

In 1987, the United States political and social systems lost trust in the judiciary and severely limited its authority by enacting the mandatory Federal Sentencing Guidelines. During this period, many judges were forced to impose sentences they viewed as unjust. Trust in the judiciary was restored in 2005, when United States v. Booker made the Sentencing Guidelines advisory. Despite the increase in judicial discretion, however, judges are still unable to correct sentences imposed during the intervening eighteen years because Booker does not apply retroactively. Unfortunately, the executive and legislative branches are similarly unable to provide adequate remedies. Congressional action is insufficient because it is inflexible, time consuming, and generally nonretroactive. Executive clemency appears more promising due to a flexible and broad nature that allows the president and state governors to pardon or commute sentences at will. But executives have become unwilling to use their clemency power, making it an inadequate remedy. This Note proposes a solution that overcomes the limitations of the current system: judicial recommendation of executive clemency. This solution produces three benefits. First, it provides judges with a discretionary tool to reduce disproportionate mandatory sentences. Second, it revitalizes the exercise of clemency by giving it additional legitimacy. Finally, it refocuses clemency grants on the defendant and the facts of the case rather than on political influences. This Note provides eight illustrative criteria for judicial recommendation of executive clemency that, together, combine the characteristics of three modern cases in which the sentencing judges recommended clemency. This Note seeks to explain how and why each criterion might be important, taking into consideration the goals of judicial discretion, executive clemency, and the criminal justice system overall

Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe

Behavior of lacunary series at the natural boundary

We develop a local theory of lacunary Dirichlet series of the form $\sum\limits_{k=1}^{\infty}c_k\exp(-zg(k)), \Re(z)>0$ as $z$ approaches the boundary i\RR, under the assumption $g'\to\infty$ and further assumptions on $c_k$. These series occur in many applications in Fourier analysis, infinite order differential operators, number theory and holomorphic dynamics among others. For relatively general series with $c_k=1$, the case we primarily focus on, we obtain blow up rates in measure along the imaginary line and asymptotic information at $z=0$. When sufficient analyticity information on $g$ exists, we obtain Borel summable expansions at points on the boundary, giving exact local description. Borel summability of the expansions provides property-preserving extensions beyond the barrier. The singular behavior has remarkable universality and self-similarity features. If $g(k)=k^b$, $c_k=1$, $b=n$ or $b=(n+1)/n$, n\in\NN, behavior near the boundary is roughly of the standard form $\Re(z)^{-b'}Q(x)$ where $Q(x)=1/q$ if x=p/q\in\QQ and zero otherwise. The B\"otcher map at infinity of polynomial iterations of the form $x_{n+1}=\lambda P(x_n)$, $|\lambda|<\lambda_0(P)$, turns out to have uniformly convergent Fourier expansions in terms of simple lacunary series. For the quadratic map $P(x) =x-x^2$, $\lambda_0=1$, and the Julia set is the graph of this Fourier expansion in the main cardioid of the Mandelbrot set

Two-component Fermi gas with a resonant interaction

We consider a two-component Fermi gas interacting via a Feshbach molecular state. It is shown that an important energy scale is $E_g=g^4m^3/(64\pi^2)$ where $g$ is the Feshbach coupling constant and $m$ the mass of the particles. Only when $E_g\gg \epsilon_{\rm F}$ where $\epsilon_{\rm F}$ is the Fermi energy can the gas be expected to enter a universal state in the unitarity limit on the atomic side of the resonance where there are no molecules present. The universal state is distinct from the molecular gas state on the other side of the resonance. We furthermore calculate the energy of the gas for this universal state and our results are related to current experiments on $^{6}$Li and $^{40}$K.Comment: 4 pages, 2 figure