On Semi-weakly n-Hyponormal Weighted Shifts

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W (alpha) with alpha (0) = alpha (1) < alpha (2) which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.

Secondary collisions revisited: real-world crash data and relationship to crash test criteria

Objectives: Previous research conducted in the late 1980s suggested that vehicle impacts following an initial barrier collision increase severe occupant injury risk. Now over 25years old, the data are no longer representative of the currently installed barriers or the present US vehicle fleet. The purpose of this study is to provide a present-day assessment of secondary collisions and to determine if current full-scale barrier crash testing criteria provide an indication of secondary collision risk for real-world barrier crashes. Methods: To characterize secondary collisions, 1,363 (596,331 weighted) real-world barrier midsection impacts selected from 13years (1997-2009) of in-depth crash data available through the National Automotive Sampling System (NASS) / Crashworthiness Data System (CDS) were analyzed. Scene diagram and available scene photographs were used to determine roadside and barrier specific variables unavailable in NASS/CDS. Binary logistic regression models were developed for second event occurrence and resulting driver injury. To investigate current secondary collision crash test criteria, 24 full-scale crash test reports were obtained for common non-proprietary US barriers, and the risk of secondary collisions was determined using recommended evaluation criteria from National Cooperative Highway Research Program (NCHRP) Report 350. Results: Secondary collisions were found to occur in approximately two thirds of crashes where a barrier is the first object struck. Barrier lateral stiffness, post-impact vehicle trajectory, vehicle type, and pre-impact tracking conditions were found to be statistically significant contributors to secondary event occurrence. The presence of a second event was found to increase the likelihood of a serious driver injury by a factor of 7 compared to cases with no second event present. The NCHRP Report 350 exit angle criterion was found to underestimate the risk of secondary collisions in real-world barrier crashes. Conclusions: Consistent with previous research, collisions following a barrier impact are not an infrequent event and substantially increase driver injury risk. The results suggest that using exit-angle based crash test criteria alone to assess secondary collision risk is not sufficient to predict second collision occurrence for real-world barrier crashes.

Quadratically Hyponormal Weighted Shifts with Recursive Tail

We characterize positive quadratic hyponormality of the weighted shift W-alpha(x) associated to the weight sequence alpha(x) : 1, 1, root x, (root u, root v, root w)(Lambda) with Stampfli recursive tail, and produce an interval in x with non-empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift. (C) 2013 Elsevier Inc. All rights reserved.

Secondary Collisions Revisited: Real-World Crash Characteristics and Relationship to Crash Test Criteria

Previous research conducted in the late 1980’s suggested that vehicle impacts following an initial barrier collision increase severe occupant injury risk. Now over twenty-five years old, the data used in the previous research is no longer representative of the currently installed barriers or US vehicle fleet. The purpose of this study is to provide a present-day assessment of secondary collisions and to determine if full-scale barrier crash testing criteria provide an indication of secondary collision risk for real-world barrier crashes. The analysis included 1,383 (596,331 weighted) real-world barrier midsection impacts selected from thirteen years (1997-2009) of in-depth crash data available through the National Automotive Sampling System (NASS) / Crashworthiness Data System (CDS). For each suitable case, the scene diagram and available scene photographs were used to determine roadside and barrier specific variables not available in NASS/CDS. Binary logistic regression models were developed for second event occurrence and resulting driver injury. Barrier lateral stiffness, post-impact vehicle trajectory, vehicle type, and pre-impact tracking conditions were found to be statistically significant contributors toward secondary event occurrence. The presence of a second event was found to increase the likelihood of a serious driver injury by a factor of seven compared to cases with no second event present. Twenty-four full-scale crash test reports were obtained for common non-proprietary US barriers, and the risk of secondary collisions was determined using recommended evaluation criteria from NCHRP Report 350. It was found that the NCHRP Report 350 exit angle criterion alone was not sufficient to predict second collision occurrence for real-world barrier crashes.

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.