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.

Anomalous Velocity Distributions in Active Brownian Suspensions

Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f (v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

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.

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Product Distributions Following Hyperthermal Collisions Between C2H4 And O(3P)

Transient Diode Laser Absorption Spectroscopy (TDLAS) was used to perform vibrational state population studies of the CO2 product from the hyperthermal reaction between C2H4 and O(3P) at room temperature using O3 as the O-atom precursor. Photodissociation of O3 using a frequency quadrupled Q-switch Nd:YAG laser pulse at 266 nm produced O(3P) atoms at high velocities which subsequently reacted with C2H4, producing several primary and secondary products including CO2. The CO2 product was detected using high-resolution TDLAS under five unique sets of reaction conditions. The vibrational distribution of the CO2 product did not follow a Boltzmann distribution at all five sets of conditions. The experiments showed a distribution in which there was a surprisingly high population in the (1000) (symmetric stretching) state compared with the other states probed, all of which contained bend excitation. In general, the CO2 population in the (1000) state was about 15-20% more populated than the Boltzmann distribution predicts. A possible explanation for this result may lie in the mechanism of CO2 evolution from the C2H4 + O(3P) reaction.

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.