Dual and triple sequence equations involving orthogonal polynomials

AbstractWe extend certain results of Richard Askey concerning dual sequence equations involving Jacobi and Laguerre polynomials to dual and triple sequence equations involving general orthogonal polynomials. We approach the problem via the polynomial expansions of Fields and Wimp, and Fields and Ismail

On solving differential and difference equations with variable coefficients

AbstractWe introduce a method of solving the functional equation ∑j = 0n ajLjf(x) = 0 where the a's are constants and L is a differential or finite difference operator that reduces the degree of a polynomial by 1

SuperWASP Observations of the 2007 Outburst of Comet 17P/Holmes

We present wide-field imaging of the 2007 outburst of Comet 17P/Holmes obtained serendipitously by SuperWASP-North on 17 nights over a 42-night period beginning on the night (2007 October 22-23) immediately prior to the outburst. Photometry of 17P's unresolved coma in SuperWASP data taken on the first night of the outburst is consistent with exponential brightening, suggesting that the rapid increase in the scattering cross-section of the coma could be largely due to the progressive fragmentation of ejected material produced on a very short timescale at the time of the initial outburst, with fragmentation timescales decreasing from t(frag)~2x10^3 s to t(frag)~1x10^3 s over our observing period. Analysis of the expansion of 17P's coma reveals a velocity gradient suggesting that the outer coma was dominated by material ejected in an instantaneous, explosive manner. We find an expansion velocity at the edge of the dust coma of v(exp) = 0.55+/-0.02 km/s and a likely outburst date of t_0=2007 October 23.3+/-0.3, consistent with our finding that the comet remained below SuperWASP's detection limit of m(V)~15 mag until at least 2007 October 23.3. Modelling of 17P's gas coma indicates that its outer edge, which was observed to extend past the outer dust coma, is best explained with a single pulse of gas production, consistent with our conclusions concerning the production of the outer dust coma.Comment: 36 pages, 8 figures, accepted for publication in MNRA

Continuous monitoring of comet Holmes from before the 2007 Outburst

The outburst and subsequent brightness evolution of comet 17P/Holmes has been observed using the MMT Observatory\u27s All-Sky Camera (Pickering 2006) on Mt. Hopkins near Tucson, Arizona, USA. The comet was picked up at the limiting visual magnitude of 5.5 on October 24.38 and tracked by the camera continuously until sunrise four hours later. During this time the comet brightened to visual magnitude 3.5. Comet Holmes was next observed just after sunset on October 25.23 at visual magnitude 2.5, where it remained approximately constant over the next three days. The comet then began to dim slowly and was followed into the early months of 2008 with periods of dense time coverage. © 2010 Springer Science+Business Media B.V

Running couplings and operator mixing in the gravitational corrections to coupling constants

The use of a running coupling constant in renormalizable theories is well known, but the implementation of this idea for effective field theories with a dimensional coupling constant is in general less useful. Nevertheless there are multiple attempts to define running couplings including the effects of gravity, with varying conclusions. We sort through many of the issues involved, most particularly the idea of operator mixing and also the kinematics of crossing, using calculations in Yukawa and lambda phi^4 theory as illustrative examples. We remain in the perturbative regime. In some theories with a high permutation symmetry, such as lambda phi^4, a reasonable running coupling can be defined. However in most cases, such as Yukawa and gauge theories, a running coupling fails to correctly account for the energy dependence of the interaction strength. As a byproduct we also contrast on-shell and off-shell renormalizaton schemes and show that operators which are normally discarded, such as those that vanish by the equations of motion, are required for off-shell renormalization of effective field theories. Our results suggest that the inclusion of gravity in the running of couplings is not useful or universal in the description of physical processes.Comment: 12 pages, 5 figure

Antimicrobial Activity of Azithromycin Encapsulated into PLGA NPs: A Potential Strategy to Overcome Efflux Resistance

Antimicrobial resistance represents a public health problem with a major negative impact on health and socioeconomic development, and is one of the biggest threats in the modern era. This requires the discovery of new approaches to control microbial infections. Nanomedicine could be one of the promising strategies to improve the treatment of microbial infections. Polymer nanoparticles (PNPs) were reported to overcome the efflux-resistant mechanism toward chemotherapeutic agents. However, to the best of our knowledge, no studies were performed to explore their ability to overcome the efflux-resistant mechanism in bacteria. In the current study, azithromycin (AZI), a macrolide antibiotic, was encapsulated into a biocompatible polymer, poly (lactic-co-glycolic acid) (PLGA) using the nano-precipitation method. The effect of the drug to polymer ratio, surfactant, and pH of the aqueous medium on particle size and drug loading percentage (DL%) were investigated in order to maximize the DL% and control the size of NPs to be around 100 nm. The antibacterial activity of AZI-PLGA NPs was investigated against AZI-resistant bacteria; Methicillin-resistant Staphylococcus aureus (MRSA) and Enterococcus faecalis (E. faecalis), where the efflux mechanism was demonstrated to be one of the resistant mechanisms. AZI-PLGA NPs were safer than free AZI, as revealed from the cytotoxicity test, and were able to overcome the efflux-resistant mechanism, as revealed by decreasing the MIC of AZI-PLGA NPs by four times than free AZI. The MIC value reduced from 256 to 64 µg/mL and from >1000 to 256 µg/mL for MRSA and E. faecalis, respectively. Therefore, encapsulation of AZI into PNPs was shown to be a promising strategy to overcome the efflux-resistant mechanism towards AZI and improve its antibacterial effect. However, future investigations are necessary to explore the effect (if any) of particle size, surface charge, and material composition of PNPs on antibacterial activity. Moreover, it is essential to ascertain the safety profiles of these PNPs, the possibility of their large-scale manufacture, and if this concept could be extended to other antibiotics