Repetitive impact exposure and characterization of stress-whitening of an American football helmet outer shell material

Mechanical stress exerted upon impact-modified polycarbonate (PC) and poly(ethylene terephthalate) (PET) blends has been reported to generate microscopic voids via rubber-toughener (RT) particle cavitation which can macroscopically manifest to visibly whiten the material. Previous work has revealed a whitening phenomenon in collegiate American football helmet outer shells after a single season and in helmet-grade plaques following linear impact testing. The purpose of this research was to quantify the effects of repetitive linear drop exposures on the (i) impact performance; (ii) physical and thermal properties; and (iii) surface and tensile mechanical properties of a stress-whitened American football helmet outer shell material. Statistically significant changes in plaque impact performance corresponded to substantial stress-whitening that penetrated up to 40–45% into the plaque thickness and elicited shifts in surface and tensile mechanical properties. Nanoscale microscopy revealed elongation of the PC/PET matrix and delamination at the RT-matrix interface. Thermal property analysis suggested the concomitant occurrence of RT cavitation and strain-induced PET crystallization. Overall, the research identified a battery of diagnostic tools to characterize material property changes of stress-whitening in rubber-toughened helmet outer shell materials.     

Infrared spectroscopy and outer product analysis for quantification of fat, nitrogen, and moisture of cocoa powder

The combination of the near infrared (NIR) and Fourier-transform infrared (FTIR) absorbance spectra (1100-2500 nm and 4000-600 cm⁻¹) of 100 cocoa powder samples was used to build calibration models for the determination of the content of fat, nitrogen, and moisture. The samples that comprised the dataset had an average composition of 13.51% of fat, 3.77% nitrogen, and 3.98% moisture. The fat content ranged from 2.42 to 22.00%, the nitrogen from 0.88 to 4.48%, and moisture from 1.60 to 7.80%. For NIR, the relative root mean square error of cross-validation (RMSECV) was 7.0% (R² = 0.96) for fat, 1.7% (R² = 0.98) for nitrogen, and 5.2% (R² = 0.94) for moisture. For FTIR, the relative RMSECV was 10.4% (R² = 0.94) for fat and 3.9% (R² = 0.95) for nitrogen. However, for moisture, it was not possible to build a calibration model with suitable predictability. The combination of the NIR and FTIR domains (data fusion) by outer product analysis PLS1 allowed to predict these parameters and to characterise frequencies in one domain based on the information of the other domain. This work allows to conclude that the second derivative of NIR is the recommended procedure to quantify fat, nitrogen, and moisture content in cocoa powders by infrared spectroscopy.     

On a class of binary linear completely transitive codes with arbitrary covering radius

An infinite class of new binary linear completely transitive (and so, completely regular) codes is given. The covering radius of these codes is growing with the length of the code. In particular, for any integer ρ≥2, there exist two codes in the constructed class with d=3, covering radius ρ and lengths and , respectively. The corresponding distance-transitive graphs, which can be defined as coset graphs of these completely transitive codes are described.     

ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract

We study the efficient set X _E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X _E ) of X _E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X _E ). Application to optimization over the efficient set for a multiple objective linear program is considered.     

Investigation of selected parameters of capillary zone electrophoresis method for analysis of isolates of outer membrane vesicles

The capillary zone electrophoresis (CZE) has recently been proposed by our group as a novel technique for outer membrane vesicles (OMVs) characterization (J. Chromatography 1621 (2020) 461047). In present work the impact of selected parameters of CZE method on OMVs isolates analysis was assessed. It was shown that the extension of sample injection plug length significantly improves the detectability of macromolecular aggregates in CZE. Moreover, a negligible adsorption of OMVs to both uncoated and polymer-modified (poly(DMA-GMA-MAPS)) capillary walls was proven. Finally, the relaxation effect as well as deformation/polarization of vesicles were demonstrated to affect OMVs electrophoretic mobility. The significance of these findings was discussed.     

Unified approach to some geometric results in variational analysis

Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting.     

An Outcome Space Branch and Bound-Outer Approximation Algorithm for Convex Multiplicative Programming

This article presents a new global solution algorithm for Convex Multiplicative Programming called the Outcome Space Algorithm. To solve a given convex multiplicative program (P _D), the algorithm solves instead an equivalent quasiconcave minimization problem in the outcome space of the original problem. To help accomplish this, the algorithm uses branching, bounding and outer approximation by polytopes, all in the outcome space of problem (P _D). The algorithm economizes the computations that it requires by working in the outcome space, by avoiding the need to compute new vertices in the outer approximation process, and, except for one convex program per iteration, by requiring for its execution only linear programming techniques and simple algebra.     

On the outer Minkowski content of sets

We provide general conditions, stable under finite unions, ensuring the existence of the outer Minkowski content of Borel subsets of . Such conditions turn out to be the same which guarantee the existence of the (d − 1)-dimensional Minkowski content of the boundary of the involved sets. Moreover, our results also apply to the study of the differentiability of the volume function of bounded sets, extending some known results in literature.      

Condition number related to the outer inverse of a complex matrix

In this paper we obtain the formula for computing the condition number of a complex matrix, which is related to the outer generalized inverse of a given matrix. We use the Schur decomposition of a matrix. We characterize the spectral norm and the Frobenius norm of the relative condition number of the generalized inverse, and the level-2 condition number of the generalized inverse. The sensitivity for the generalized Drazin-inverse solution of linear systems is presented. We also present the structured perturbation of the generalized inverse.