The D4D_4 Root System is Not Universally Optimal

We prove that the $D_4$ root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in $S^3$, based on numerical computations suggesting that every 5-design consisting of 24 points in $S^3$ is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the $D_4$ root system.Mathematic

Optimal asymptotic bounds for spherical designs

"Vegeu el resum a l'inici del document del fitxer adjunt"

Energy on spheres and discreteness of minimizing measures

In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the p-frame energy has empty interior whenever p is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials

Full modeling and experimental validation of cylindrical holographic lenses recorded in Bayfol HX photopolymer and partly operating in the transition regime for solar concentration

Concentrating photovoltaics for building integration can be successfully carried out with Holographic Optical Elements (HOEs) because of their behavior analogous to refractive optical elements and their tuning ability to the spectral range that the photovoltaic (PV) cell is sensitive to. That way, concentration of spectral ranges that would cause overheating of the cell is avoided. Volume HOEs are usually chosen because they provide high efficiencies. However, their chromatic selectivity is also very high, and only a small part of the desired spectral range reaches the PV cell. A novel approach is theoretically and experimentally explored to overcome this problem: the use of HOEs operating in the transition regime, which yield lower chromatic selectivity while keeping rather high efficiencies. A model that considers the recording material’s response, by determining the index modulation reached for each spatial frequency and exposure dosage, has been developed. It has been validated with experimental measurements of three cylindrical holographic lenses with different spatial frequency ranges recorded in Bayfol HX photopolymer. Simulations of systems comprising two lenses and a mono-c Si PV cell are carried out with the standard AM 1.5D solar spectrum. Promising results are obtained when using the system with lower spatial frequencies lenses: a total current intensity equal to 3.72 times the one that would be reached without the concentrator.Generalitat de Catalunya (2017FI_B2_00127); Ministerio de Economía y Competitividad of Spain (ENE2013-48325-R, ENE2016-81040-R); Diputación General de Aragón - Fondo Social Europeo (TOL research group, T76); Universidad de Zaragoza (UZ2017-CIE-02)

Publications of the Jet Propulsion Laboratory, July 1964 through June 1965

JPL publications bibliography with abstracts - reports on DSIF, Mariner program, Ranger project, Surveyor project, and other space programs, and space science

Canonical duality theory and algorithm for solving bilevel knapsack problems with applications

A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved analytically in term of their canonical dual solutions. The existence and uniqueness of these analytical solutions are proved. NP-hardness of the knapsack problems is discussed. A powerful CDT algorithm combined with an alternative iteration and a volume reduction method is proposed for solving the NP-hard bilevel knapsack problems. Application is illustrated by benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. © 2013 IEEE