Implicit Racial Biases in Prosecutorial Summations: Proposing an Integrated Response

Racial bias has evolved from the explicit racism of the Jim Crow era to amore subtle and difficult-to-detect form: implicit racial bias. Implicit racial biases exist unconsciously and include negative racial stereotypes andassociations. Everyone, including actors in the criminal justice system who believe themselves to be fair, possess these biases. Although inaccessible through introspection, implicit biases can easily be triggered through language. When trials involve Black defendants, prosecutors’ summations increasingly include racial themes that could trigger jurors’ implicit biases, lead to the perpetuation of unfair stereotypes, and contribute to racial injustice and disparate outcomes. This Note examines and critiques the current approaches that courts and disciplinary authorities use to address implicit racial biases in prosecutorial summations. Recognizing the inadequacy in these current methods, this Note proposes an integrated response, which involves lawyers, jurors, trial courts, and appellate courts. The proposed approach seeks to increase recognition of implicit racial bias use, deter prosecutors from using language that triggers implicit racial biases, and ensure that Black defendants’ equal protection rights are upheld

Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 10-phi-9 transformation. From this result, we deduce new multivariable terminating 10-phi-9 transformations, 8-phi-7 summations and other identities. We also use similar methods to derive new multivariable 1-psi-1 summations. Some of our results are extended to the case of elliptic hypergeometric series.Comment: 29 pages, minor changes; to appear in Indag. Math., special volume dedicated to Tom Koornwinde

Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems

In this paper, we derive the Ewald method for inverse power-law interactions in quasi-two dimensional systems. The derivation is done by using two different analytical methods. The first uses the Parry's limit, that considers the Ewald methods for quasi-two dimensional systems as a limit of the Ewald methods for tridimensional systems, the second uses Poisson-Jacobi identities for lattice sums. Taking into account the equivalence of both derivations, we obtain a new analytical Fourier transform intregral involving incomplete gamma function. Energies of the generalized restrictive primitive model of electrolytes ($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) are given for the tridimensional, quasi-two dimensional and monolayers systems. Few numerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCP monolayers systems are reported.Comment: to be published in Journal of Physics A: Mathematical and Theoretical (19 pages, 2 figures and 3 tables

Cusp Summations and Cusp Relations of Simple Quad Lenses

We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total images of a given source is a constant, we calculate the cusp summations for the five lens models. We find that the cusp summations are always larger than 0 for source on the major cusps, while can be larger or smaller than 0 for source on the minor cusps. We also find that if these lenses tend to the circular lens, the major and minor cusp summations will have infinite values, and with positive and negative signs respectively. The cusp summations do not change significantly if the sources are slightly deviated from the cusps. In addition, through the magnification invariants, we also derive the analytical signed cusp relations on the axes for three lens models. We find that both on the major and the minor axes the larger the lenses deviated from the circular lens, the larger the signed cusp relations. The major cusp relations are usually larger than the absolute minor cusp relations, but for some lens models with very large deviation from circular lens, the minor cusp relations can be larger than the major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA

Bilateral identities of the Rogers-Ramanujan type

We derive by analytic means a number of bilateral identities of the Rogers-Ramanujan type. Our results include bilateral extensions of the Rogers-Ramanujan and the G\"ollnitz-Gordon identities, and of related identities by Ramanujan, Jackson, and Slater. We give corresponding results for multiseries including multilateral extensions of the Andrews-Gordon identities, of Bressoud's even modulus identities, and other identities. The here revealed closed form bilateral and multilateral summations appear to be the very first of their kind. Given that the classical Rogers-Ramanujan identities have well-established connections to various areas in mathematics and in physics, it is natural to expect that the new bilateral and multilateral identities can be similarly connected to those areas. This is supported by concrete combinatorial interpretations for a collection of four bilateral companions to the classical Rogers-Ramanujan identities.Comment: 25 page