A note on log-convexity of q-Catalan numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted

Protective telescoping shield for solar concentrator

An apparatus is described for use with a solar concentrator such as a parabolic dish which concentrates sunlight onto a small opening of a solar receiver, for protecting the receiver in the event of a system failure that could cause concentrated sunlight to damage the receiver. The protective apparatus includes a structure which can be moved to a stowed position where it does not block sunlight, to a deployed position. In this position, the structure forms a tube which substantially completely surrounds an axis connecting the receiver opening to the center of the concentrator at locations between the receiver and the concentrator

Diversity and Security in UK Electricity Generation: The Influence of Low Carbon Objectives

We explore the relationship between low carbon objectives and the strategic security of electricity in the context of the UK Electricity System. We consider diversity of fuel source mix to represent one dimension of security - robustness against interruptions of any one source - and apply two different diversity indices to the range of electricity system scenarios produced by the UK government and independent researchers. Using data on wind generation we also consider whether a second dimension of security - the reliability of generation availability - is compromised by intermittency of renewable generation. Our results show that low carbon objectives are uniformly associated with greater long-term diversity in UK electricity. We discuss reasons for this result, explore sensitivities, and briefly discuss possible policy instruments associated with diversity and their limitations.Diversity, Security, Low Carbon, Wind Generation, Electricity

Calibration results for the GEOS-3 altimeter

Data from the GEOS-3 altimeter were analyzed, for both the intensive and global modes, to determine the altitude bias levels for each mode and to verify the accuracy of the time tags which have been applied to the data. The best estimates of the biases are -5.30 + or - .2 m (intensive mode) and -3.55 m + or - .4 m (global mode). These values include the approximately 1.6 m offset of the altimeter antenna focal point from the GEOS-3 spacecraft center-of-mass. The negative signs indicate that the measured altitudes are too short. The data is corrected by subtracting the above bias numbers for the respective modes. Timing corrections which should be applied to the altimeter data were calculated theoretically, and subsequently confirmed through crossover analysis for passes 6-8 revolutions apart. The time tag correction that should be applied consists of -20.8 msec + 1 interpulse period (10.240512 msec)

Tackifier for addition polyimides

A modification to the addition polyimide, LaRC-160, was prepared to improve tack and drape and increase prepeg out-time. The essentially solventless, high viscosity laminating resin is synthesized from low cost liquid monomers. The modified version takes advantage of a reactive, liquid plasticizer which is used in place of solvent and helps solve a major problem of maintaining good prepeg tack and drape, or the ability of the prepeg to adhere to adjacent plies and conform to a desired shape during the lay up process. This alternate solventless approach allows both longer life of the polymer prepeg and the processing of low void laminates. This approach appears to be applicable to all addition polyimide systems

C-Cl Bond Fission, Hcl Elimination, And Secondary Radical Decomposition In The 193 Nm Photodissociation Of Allyl Chloride

The primary photodissociation dynamics of allyl chloride upon excitation at 193 nm is investigated in a crossed laser-molecular beam scattering apparatus. Tunable vacuum ultraviolet (VUV) photoionization of the products provides a unique ability to learn about the secondary reaction products of the nascent photoproducts formed. The data show evidence for four significant primary reaction channels: a previously unidentified low kinetic energy C-Cl bond fission channel producing unstable allyl radicals, an excited state C-Cl bond fission channel producing Cl atoms with high translational energy, an HCl elimination pathway releasing significant energy to product translation to HCl and its momentum-matched mass 40 partner, and an HCl elimination channel producing low kinetic energy HCl products and predominantly unstable mass 40 products. The measured branching of these primary reaction channels of [all C-Cl] : [fast C-Cl] : [slow C-Cl] : [fast HCl] : [slow HCl] : [all HCl] is 1.00: 0.971: 0.029: 0.291: 0.167: 0.458 (where fast refers to the high recoil kinetic energy channels). The high internal energy allyl radicals formed in the slow C-Cl fission pathway of allyl chloride further dissociate/isomerize, as do the unstable mass 40 products formed in the HCl elimination pathways, and these products are investigated. Photoionization efficiency (PIE) curves of the HCl product suggest that a three-centered elimination mechanism contributes significantly to an observed HCl elimination reaction. (C) 2002 American Institute of Physics

Pathways to Economic Mobility: Key Indicators

Outlines how indicators of social, human, and financial capital affect an individual's chances of moving up or down the economic ladder. Analyzes data on family structure, community, education, race/ethnicity, health, home ownership, and other factors

Not All Antibodies Are Created Equal: Factors That Influence Antibody Mediated Rejection.

Consistent with Dr. Paul Terasaki's "humoral theory of rejection" numerous studies have shown that HLA antibodies can cause acute and chronic antibody mediated rejection (AMR) and decreased graft survival. New evidence also supports a role for antibodies to non-HLA antigens in AMR and allograft injury. Despite the remarkable efforts by leaders in the field who pioneered single antigen bead technology for detection of donor specific antibodies, a considerable amount of work is still needed to better define the antibody attributes that are associated with AMR pathology. This review highlights what is currently known about the clinical context of pre and posttransplant antibodies, antibody characteristics that influence AMR, and the paths after donor specific antibody production (no rejection, subclinical rejection, and clinical dysfunction with AMR)

From Event-B models to Dafny code contracts

International audienceThe constructive approach to software correctness aims at formal modelling and verification of the structure and behaviour of a system in different levels of abstraction. In contrast, the analytical approach to software verification focuses on code level correctness and its verification. Therefore it would seem that the constructive and analytical approaches should complement each other well. To demonstrate this idea we present a case for linking two existing verification methods, Event-B (constructive) and Dafny (analytical). This approach combines the power of Event-B abstraction and its stepwise refinement with the verification capabilities of Dafny. We presented a small case study to demonstrate this approach and outline of the rules for transforming Event-B events to Dafny contracts. Finally, a tool for automatic generation of Dafny contracts from Event-B formal models is presented