Monodromy Substitutions and Rational Blowdowns

We introduce several new families of relations in the mapping class groups of planar surfaces, each equating two products of right-handed Dehn twists. The interest of these relations lies in their geometric interpretation in terms of rational blowdowns of 4-manifolds, specifically via monodromy substitution in Lefschetz fibrations. The simplest example is the lantern relation, already shown by the first author and Gurtas to correspond to rational blowdown along a -4 sphere; here we give relations that extend that result to realize the "generalized" rational blowdowns of Fintushel-Stern and Park by monodromy subsitution, as well as several of the families of rational blowdowns discovered by Stipsicz-Szab\'o-Wahl.Comment: 28 pages, many figures. v2: minor edits; this version accepted for publication in Journal of Topolog

Method and apparatus for a substantially coaxial injector element

A system to provide a two piece robust fluid injector. According to various embodiments, the fluid injector is a fuel injector for a combustion engine. The injector includes two coaxially formed annuluses. One annulus is formed in a face plate and the second annulus or hole is defined by a tube extending through the face plate. The tube extends through the face plate in a portion of a through bore which also is used to define the second annulus. The second annulus is formed using a throughbore through which the tube extends. This allows the second annulus to always be formed inherently and precisely substantially coaxial with the first annulus. Moreover, the second annulus can be formed with a much greater tolerance than if other independent components needed to be added

Dynamic scheduling of recreational rental vehicles with revenue management extensions

The rental fleet scheduling problem (RFSP) arises in vehicle-rental operations that offer a wide variety of vehicle types to customers, and allow a rented vehicle to migrate to a setdown depot other than the pickup depot. When there is a shortage of vehicles of a particular type at a depot, vehicles may be relocated to that depot, or vehicles of similar types may be substituted. The RFSP involves assigning vehicles to rentals so as to minimise the costs of these operations, and arises in both static and online contexts. The authors have adapted a well-known assignment algorithm for application in the online context. In addition, a network-flow algorithm with more comprehensive coverage of problem conditions is used to investigate the determination of rental pricing using revenue management principles. The paper concludes with an outline of the algorithms use in supporting the operations of a large recreational vehicle rental company

Planetary ring studies

The following topics are covered: (1) characterization of the fine scale structure in Saturn's A and B rings; (2) ballistic transport modeling and evolution of fine ring structure; (3) faint features in the rings of Saturn; (4) the Encke moonlet; (5) dynamics in ringmoon systems; (6) a nonclassical radiative transfer model; and (7) particle properties from stellar occultation data

Coaxial Propellant Injectors With Faceplate Annulus Control

An improved design concept for coaxial propellant injectors for a rocket engine (or perhaps for a non-rocket combustion chamber) offers advantages of greater robustness, less complexity, fewer parts, lower cost, and less bulk, relative to prior injectors of equivalent functionality. This design concept is particularly well suited to small, tight-tolerance injectors, for which prior designs are not suitable because the practical implementation of those designs entails very high costs and difficulty in adhering to the tolerances

Epidural Analgesia Decreases Narcotic Requirements in Low Level Spina Bifida Patients Undergoing Urologic Laparotomy for Neurogenic Bladder and Bowel

Purpose Concern of anatomical anomalies and worsening neurologic symptoms has prevented widespread use of epidural catheters in patients with low level spina bifida (LLSB). We hypothesize that thoracic epidural placement in the T9-T10 interspace is safe and decreases narcotic requirements in LLSB patients following major open lower urinary tract reconstruction (LUTR). Materials and Methods We reviewed consecutive LLSB patients who had LUTR and epidurals for post-operative pain control. Controls were LLSB patients who received single shot transversus abdominis plane (TAP) blocks with similar procedures. Complications from epidural placement, including changes in motor and sensory status were recorded. Opioid consumption was calculated utilizing equivalent IV morphine doses. Mean and maximum pain scores on post-operative day (POD) 0-3 were calculated. Results 10 LLSB patients who had lower urinary tract reconstruction and epidurals were matched to 10 LLSB patients who had lower urinary tract reconstruction and transverse abdominis plane blocks. Groups were demographically similar. All had full abdominal sensation and functional levels at or below L3. No epidural complications or changes in neurological status were noted. The epidural group had decreased opioid consumption on POD 0-3 (0.75 mg/kg vs. 1.29 mg/kg, p=0.04). Pain scores were similar or improved in the epidural group. Conclusions Thoracic epidural analgesia appears to be a safe and effective opioid sparing option to assist with post-operative pain management following lower urinary tract reconstruction in LLSB patients